2,492 results
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152. EXISTENCE AND STABILITY OF SOLUTION IN BANACH SPACE FOR AN IMPULSIVE SYSTEM INVOLVING ATANGANA–BALEANU AND CAPUTO–FABRIZIO DERIVATIVES.
- Author
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AL-SADI, WADHAH, WEI, ZHOUCHAO, MOROZ, IRENE, and ALKHAZZAN, ABDULWASEA
- Subjects
- *
BANACH spaces , *NONLINEAR differential equations , *INTEGRAL equations , *NONLINEAR operators , *IMPULSIVE differential equations , *FRACTIONAL differential equations - Abstract
This paper investigates the necessary conditions relating to the existence and uniqueness of solution to impulsive system fractional differential equation with a nonlinear p-Laplacian operator. Our problem is based on two kinds of fractional order derivatives. That is, Atangana–Baleanu–Caputo (ABC) fractional derivative and the Caputo–Fabrizio derivative. To achieve our main aims, we will first convert the proposed impulse system into an integral equation form. Next, we prove the existence and uniqueness of solutions with the help of Leray–Schauder's theory and the Banach contraction principle. We analyze the operator for continuity, boundedness, and equicontinuity. Further, we investigate the stability solution to the proposed impulsive system by using stability techniques. In the last part, we demonstrate the results via an illustrative example for the application of the results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
153. Convergence Results for Nonlinear Sampling Kantorovich Operators in Modular Spaces.
- Author
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Costarelli, Danilo, Natale, Mariarosaria, and Vinti, Gianluca
- Subjects
- *
ORLICZ spaces , *NONLINEAR operators , *INTEGRAL representations , *FUNCTION spaces - Abstract
In the present paper, convergence in modular spaces is investigated for a class of nonlinear discrete operators, namely the nonlinear multivariate sampling Kantorovich operators. The convergence results in the Musielak-Orlicz spaces, in the weighted Orlicz spaces, and in the Orlicz spaces follow as particular cases. Even more, spaces of functions equipped by modulars without an integral representation are presented and discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
154. CONVERGENCE, OPTIMAL POINTS AND APPLICATIONS.
- Author
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SHARMA, SHAGUN and CHANDOK, SUMIT
- Subjects
- *
STOCHASTIC convergence , *LINEAR operators , *MATHEMATICS , *FIXED point theory , *NONLINEAR operators - Abstract
In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
155. ON THE EXISTENCE OF SOLUTIONS FOR AN INFINITE SYSTEM OF INTEGRAL EQUATIONS.
- Author
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MEFTEH, BILEL
- Subjects
- *
INFINITY (Mathematics) , *BANACH algebras , *BANACH spaces , *INTEGRALS , *FIXED point theory , *NONLINEAR operators - Abstract
The paper is devoted to prove the existence of solutions for an infinite system of non- linear integral equations. This system is investigated in the WC-Banach algebra C(I; c0), the space of all continuous functions acting from an interval I into the sequence space c0. Making use of the measure of weak noncompactness and the weak topology, we establish some fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operat- ors acting onWC-Banach algebra involving w-contractive operators. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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156. Study of Solutions for a Degenerate Reaction Equation with a High Order Operator and Advection.
- Author
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Díaz Palencia, José Luis, Roa González, Julián, and Sánchez Sánchez, Almudena
- Subjects
ADVECTION ,ADVECTION-diffusion equations ,NONLINEAR operators ,OSCILLATING chemical reactions ,EQUATIONS - Abstract
The goal of the present study is to characterize solutions under a travelling wave formulation to a degenerate Fisher-KPP problem. With the degenerate problem, we refer to the following: a heterogeneous diffusion that is formulated with a high order operator; a non-linear advection and non-Lipstchitz spatially heterogeneous reaction. The paper examines the existence of solutions, uniqueness and travelling wave oscillatory properties (also called instabilities). Such oscillatory behaviour may lead to negative solutions in the proximity of zero. A numerical exploration is provided with the following main finding to declare: the solutions keeps oscillating in the proximity of the null stationary solution due to the high order operator, except if the reaction term is quasi-Lipschitz, in which it is possible to define a region where solutions are positive locally in time. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
157. SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations.
- Author
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Gong, Chunye, She, Mianfu, Yuan, Wanqiu, and Zhao, Dan
- Subjects
SCHRODINGER equation ,FRACTIONAL differential equations ,SOBOLEV spaces ,FIXED point theory ,NONLINEAR operators - Abstract
In this paper, a fully discrete scheme is proposed to solve the nonlinear Schrödinger-Possion equations. The scheme is developed by the scalar auxiliary variable (SAV) approach, the Crank-Nicolson temproal discretization and the Galerkin-Legendre spectral spatial discretization. The fully discrete scheme is proved to be mass- and energy- conserved. Moreover, unconditional energy stability and convergence of the scheme are obtained by the use of the Gagliardo-Nirenberg and some Sobolev inequalities. Numerical results are presented to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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158. Hölder-Logarithmic type approximation for nonlinear backward parabolic equations connected with a pseudo-differential operator.
- Author
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Hai, Dinh Nguyen Duy
- Subjects
PSEUDODIFFERENTIAL operators ,SOBOLEV spaces ,NONLINEAR equations ,HEAT equation ,EQUATIONS ,NONLINEAR operators - Abstract
In this paper, we deal with the backward problem for nonlinear parabolic equations involving a pseudo-differential operator in the n-dimensional space. We prove that the problem is ill-posed in the sense of Hadamard, i.e., the solution, if it exists, does not depend continuously on the data. To regularize the problem, we propose two modified versions of the so-called optimal filtering method of Seidman [T.I. Seidman, Optimal filtering for the backward heat equation, SIAM J. Numer. Anal., 33 (1996), 162–170]. According to different a priori assumptions on the regularity of the exact solution, we obtain some sharp optimal estimates of the Hölder-Logarithmic type in the Sobolev space H
q (Rn ). [ABSTRACT FROM AUTHOR]- Published
- 2022
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159. The penalty method for generalized mixed variational-hemivariational inequality problems.
- Author
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SHIH-SEN CHANG, SALAHUDDIN, AHMADINI, A. A. H., WANG, L., and WANG, G.
- Subjects
NONLINEAR boundary value problems ,CONTACT mechanics ,DIFFERENTIAL operators ,BANACH spaces ,NONLINEAR operators - Abstract
It is well known that many popular variational, quasi-variational, hemivariational inequalities and variational inclusions involving constraints in a Banach space to convert a fixed point problems for finding the solution of such problems. This paper is to infuse a sequence of penalized problems without constraints and we show under the few reasonable assumptions to the Kuratowski upper limit with respect to the weak topology of the sets of solutions to penalized problems is nonempty. As an application, we explore two complicated partial differential systems of elliptic mixed boundary value problem involving a nonlinear nonhomogeneous differential operator with an obstacle effect, and a nonlinear elastic contact problem in mechanics with unilateral constraints. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
160. Risk Assessment of EPB Shield Construction Based on the Nonlinear FAHP Method.
- Author
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Wang, Xueyan, Gong, Hang, Song, Qiyu, Yan, Xiao, and Luo, Zheng
- Subjects
RISK assessment ,ANALYTIC hierarchy process ,EARTH pressure ,NONLINEAR operators ,LINEAR statistical models ,ECOLOGICAL risk assessment - Abstract
There are many risk factors in EPB shield construction. The traditional fuzzy analytic hierarchy process (FAHP) method usually uses a linear analysis method to determine the risk level, but there are often some risk factors with prominent influence, which will reduce the accuracy of the evaluation results. In this paper, a new risk assessment model of Earth pressure balance (EPB) shield construction based on a nonlinear FAHP method is established by introducing nonlinear factors into the comprehensive calculation of the traditional FAHP. First, the new model establishes the framework of EPB shield construction risk analysis based on the work breakdown structure (WBS) and risk breakdown structure (RBS) methods. Then, it constructs an EPB shield construction risk index system by coupling the units of the WBS and RBS. The model constructs a fuzzy consistent judgment matrix, which replaces the 1∼9 scale. Finally, the nonlinear operator is introduced into the FAHP comprehensive calculation, considering the influence of some prominent risk factors, which improves the accuracy of the risk assessment. By applying the new model to the risk analysis of the EPB shield construction section of a tunnel project in Hangzhou, the effectiveness of the model is further verified. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
161. REMARKS ON THE RANGE AND THE KERNEL OF GENERALIZED DERIVATION.
- Author
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BOUHAFSI, Y., ECH-CHAD, M., MISSOURI, M., and ZOUAKI, A.
- Subjects
ALGEBRA ,HILBERT space ,NONLINEAR operators ,COMPACT operators ,MATHEMATICAL equivalence ,MATRICES (Mathematics) - Abstract
Let L(H) denote the algebra of operators on a complex infinite dimensional Hilbert space H and let J denote a two-sided ideal in L(H). Given A,B ∈ L(H), define the generalized derivation δ
A,B as an operator on L(H) by δA,B (X) = AX - XB. We say that the pair of operators (A,B) has the Fuglede-Putnam property (PF)J if AT = TB and T ∈ J implies A*T = TB*. In this paper, we give operators A,B for which the pair (A,B) has the property (PF)J. We establish the orthogonality of the range and the kernel of a generalized derivation δA,B for non-normal operators A,B ∈ L(H). We also obtain new results concerning the intersection of the closure of the range and the kernel of δA,B. [ABSTRACT FROM AUTHOR]- Published
- 2022
- Full Text
- View/download PDF
162. Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces.
- Author
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Bahidi, Fatima, Krichen, Bilel, and Mefteh, Bilel
- Subjects
NONLINEAR equations ,OPERATOR equations ,NONLINEAR integral equations ,NONLINEAR operators ,MATRICES (Mathematics) ,COMPOSITION operators - Abstract
The purpose of this paper is to prove some fixed point results dealing with a system of nonlinear equations defined in an angelic Hausdorff locally convex space (X , { | ⋅ | p } p ∈ Λ) (X,\{\lvert\,{\cdot}\,\rvert_{p}\}_{p\in\Lambda}) having the 휏-Krein–Šmulian property, where 휏 is a weaker Hausdorff locally convex topology of 푋. The method applied in our study is connected with a family Φ Λ τ \Phi_{\Lambda}^{\tau} -MNC of measures of weak noncompactness and with the concept of 휏-sequential continuity. As a special case, we discuss the existence of solutions for a 2 × 2 2\times 2 block operator matrix with nonlinear inputs. Furthermore, we give an illustrative example for a system of nonlinear integral equations in the space C (R +) × C (R +) C(\mathbb{R}^{+})\times C(\mathbb{R}^{+}) to verify the effectiveness and applicability of our main result. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
163. Caccioppoli-type inequalities for Dirac operators.
- Author
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Kashkynbayev, Ardak and Oralsyn, Gulaiym
- Subjects
DIRAC operators ,NONLINEAR differential equations ,NONLINEAR operators - Abstract
In this paper, we establish the Caccioppoli estimates for the nonlinear differential equation − D ‾ (| D v | p − 2 D v) = λ | v | p − 2 v , 1 < p < ∞ , where D is the Dirac operator. Moreover, we obtain general weighted versions of the Caccioppoli-type inequalities for the Dirac operators. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
164. Tykhonov well-posedness of a mixed variational problem.
- Author
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Cai, Dong-ling, Sofonea, Mircea, and Xiao, Yi-bin
- Subjects
NONLINEAR operators ,LAGRANGE multiplier ,NONLINEAR equations - Abstract
We consider a mixed variational problem governed by a nonlinear operator and a set of constraints. Existence, uniqueness and convergence results for this problem have already been obtained in the literature. In this current paper we complete these results by proving the well-posedness of the problem, in the sense of Tykhonov. To this end we introduce a family of approximating problems for which we state and prove various equivalence and convergence results. We illustrate these abstract results in the study of a frictionless contact model with elastic materials. The process is assumed to be static and the contact is with unilateral constraints. We derive a weak formulation of the model which is in the form of a mixed variational problem with unknowns being the displacement field and the Lagrange multiplier. Then, we prove various results on the corresponding mixed problem, including its well-posedness in the sense of Tykhonov, under various assumptions on the data. Finally, we provide mechanical interpretation of our results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
165. Global Dynamics of a Diffusive Leslie-Gower Predator-prey Model with Fear Effect.
- Author
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Zebin Fang, Shanshan Chen, and Junjie Wei
- Subjects
FEAR Effect (Game) ,ANALYTICAL mechanics ,POPULATION density ,FIXED point theory ,NONLINEAR operators - Abstract
A diffusive Leslie-Gower predator-prey model with fear effect is considered in this paper. For the kinetic system, we show that the unique positive equilibrium is globally asymptotically stable. Moreover, we find that high levels of fear could decrease the population densities of both prey and predator in a long time. For the diffusive model, we obtain the similar results under certain conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
166. A genetic programming based system for the automatic construction of image filters.
- Author
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Pedrino, E.C., Roda, V.O., Kato, E.R.R., Saito, J.H., Tronco, M.L., Tsunaki, R.H., Morandin Jr., O., and Nicoletti, M.C.
- Subjects
IMAGE processing ,GENETIC programming ,AUTOMATION ,NONLINEAR operators ,LINEAR operators ,IMAGE representation ,PATTERN recognition systems - Abstract
The manual selection of linear and nonlinear operators for producing image filters is not a trivial task in practice, so new proposals that can automatically improve and speed up the process can be of great help. This paper presents a new proposal for constructing image filters using an evolutionary programming approach, which has been implemented as the IFbyGP software. IFbyGP employs a variation of the Genetic Programming algorithm (GP) and can be applied to binary and gray level image processing. A solution to an image processing problem is represented by IFbyGP as a set of morphological, convolution and logical operators. The method has a wide range of applications, encompassing pattern recognition, emulation filters, edge detection, and image segmentation. The algorithm works with a training set consisting of input images, goal images, and a basic set of instructions supplied by the user, which would be suitable for a given application. By making the choice of operators and operands involved in the process more flexible, IFbyGP searches for the most efficient operator sequence for a given image processing application. Results obtained so far are encouraging and they stress the feasibility of the proposal implemented by IFbyGP. Also, the basic language used by IFbyGP makes its solutions suitable to be directly used for hardware control, in a context of evolutionary hardware. Although the proposal implemented by IFbyGP is general enough for dealing with binary, gray level and color images, only applications using the first two are considered in this paper; as it will become clear in the text, IFbyGP aims at the direct use of induced sequences of operations by hardware devices. Several application examples discussing and comparing IFbyGP results with those obtained by other methods available in the literature are presented and discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
167. EXISTENCE AND STABILITY RESULTS FOR COINCIDENCE POINTS OF NONLINEAR CONTRACTIONS.
- Author
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Choudhury, Binayak S., Metiya, Nikhilesh, and Kundu, Sunirmal Kundu
- Subjects
NONLINEAR operators ,MATHEMATICAL mappings - Abstract
In this paper we define-admissibility of multi-valued mapping with respect to a single-valued mapping and use this concept to establish a coincidence point theorem for pairs of nonlinear multi-valued and single-valued mappings under the assumption of an inequality with rational terms. We illustrate the result with an example. In the second part of the paper we prove the stability of the coincidence point sets associated with the pairs of mappings in our coincidence point theorem. For that purpose we define the corresponding stability concepts of coincidence points. The results are primarily in the domain of nonlinear set-valued analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
168. Fixed point results for generalized Θ-contractions.
- Author
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Ahmad, Jamshaid, Al-Mazrooei, Abdullah E., Yeol Je Cho, and Young-Oh Yang
- Subjects
FIXED point theory ,NONLINEAR operators ,CONTRACTIONS (Topology) ,TOPOLOGICAL spaces ,TOPOLOGY - Abstract
The aim of this paper is to extend the result of [M. Jleli, B. Samet, J. Inequal. Appl., 2014 (2014), 8 pages] by applying a simple condition on the function Θ. With this condition, we also prove some fixed point theorems for Suzuki-Berinde type Θ-contractions which generalize various results of literature. Finally, we give one example to illustrate the main results in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
169. Machine learning for a class of partial differential equations with multi-delays based on numerical Gaussian processes.
- Author
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Zhang, Wenbo and Gu, Wei
- Subjects
- *
GAUSSIAN processes , *PARTIAL differential equations , *MACHINE learning , *RUNGE-Kutta formulas , *LATENT variables , *DELAY differential equations , *NONLINEAR operators - Abstract
Delay partial differential equations (PDEs) are widely utilized in many fields, such as climate prediction and epidemiology. But observation data in real world is often noisy and discrete. And in order to expand the applications of delay PDEs, we consider numerical Gaussian processes to solve these models. In this paper, numerical Gaussian processes for predicting the latent solution of a type of delay PDEs with multi-delays are investigated, and various delay PDEs are studied, including problems governed by variable-order fractional order operators and nonlinear operators, so as to adapt to the needs of practical applications. Numerical Gaussian processes are very good at fitting latent solution of PDEs, when all observation data is noisy and discontinuous. And the methodology can clearly quantify the uncertainty of the predicted solution. For complex boundaries controlled by ODEs, we consider mixed boundary conditions of delay PDEs in this paper. And we also apply Runge-Kutta methods to enhance the prediction accuracy of these problems. Finally, we design seven numerical examples to investigate the efficiency of NGPs and how the noisy data influences the solution of our studied problems. • Numerical Gaussian processes for solving delay PDEs models governed by variable-order fractional order operators and nonlinear operators. • Numerical Gaussian processes are very good at fitting latent solution of PDEs, when all observation data is noisy and discontinuous. • Runge-Kutta methods are applied to enhance the prediction accuracy of these problems. • Seven numerical examples to investigate the efficiency of NGPs and how the noisy data influences the solution of our studied problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
170. Gradient Cepstrum Combined with Simplified Extreme Channel Prior for Blind Deconvolution.
- Author
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Liu, Jing, Tan, Jieqing, and He, Lei
- Subjects
NONLINEAR operators ,DECONVOLUTION (Mathematics) ,IMAGE processing - Abstract
As a well-known ill-conditional problem in the image processing field, image deblurring has become a hot topic recently. The prior-based blind image deblurring methods have recently shown promising effectiveness. A lot of advanced algorithms such as dark channel prior, bright channel prior, and local maximum gradient prior are time-consuming since nonlinear operators are involved. Presented in this paper is a fast blind image deblurring algorithm which uses the simplified extreme channel prior (SECP) and gradient cepstrum. The inspiration for this work comes from the fact that the simplified bright channel prior (SBCP) of the clear image has fewer non-one elements than the blurred one. We propose a novel SECP based on the proposed SBCP and the simplified dark channel prior (SDCP). By enforcing the L 0 norm constraint to the terms involving SECP and incorporating them into the traditional deblurring framework, an effective optimization scheme is explored. Furthermore, gradient cepstrum is used to determine the size of the initial kernel and restrain excessive iterations in each scale. Experimental results illustrate that our algorithm outperforms the state-of-the-art deblurring algorithms in terms of computational efficiency and deblurring effect on both benchmark datasets and real-world blur scenes. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
171. Power Normalizations in Fine-Grained Image, Few-Shot Image and Graph Classification.
- Author
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Koniusz, Piotr and Zhang, Hongguang
- Subjects
COVARIANCE matrices ,NONLINEAR operators ,DEEP learning ,LAPLACIAN matrices ,CLASSIFICATION ,CHARTS, diagrams, etc. ,FEATURE extraction - Abstract
Power Normalizations (PN) are useful non-linear operators which tackle feature imbalances in classification problems. We study PNs in the deep learning setup via a novel PN layer pooling feature maps. Our layer combines the feature vectors and their respective spatial locations in the feature maps produced by the last convolutional layer of CNN into a positive definite matrix with second-order statistics to which PN operators are applied, forming so-called Second-order Pooling (SOP). As the main goal of this paper is to study Power Normalizations, we investigate the role and meaning of MaxExp and Gamma, two popular PN functions. To this end, we provide probabilistic interpretations of such element-wise operators and discover surrogates with well-behaved derivatives for end-to-end training. Furthermore, we look at the spectral applicability of MaxExp and Gamma by studying Spectral Power Normalizations (SPN). We show that SPN on the autocorrelation/covariance matrix and the Heat Diffusion Process (HDP) on a graph Laplacian matrix are closely related, thus sharing their properties. Such a finding leads us to the culmination of our work, a fast spectral MaxExp which is a variant of HDP for covariances/autocorrelation matrices. We evaluate our ideas on fine-grained recognition, scene recognition, and material classification, as well as in few-shot learning and graph classification. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
172. Controllability for abstract semilinear control systems with homogeneous properties.
- Author
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Jeong, Jin-Mun, Son, Sang-Jin, and Park, Ah-Ran
- Subjects
NONLINEAR operators ,SET-valued maps ,OPERATOR equations ,NONLINEAR equations ,SURJECTIONS ,CARLEMAN theorem - Abstract
This paper considers the approximate controllability for a class of abstract semilinear control systems using a method called surjectivity theorems for nonlinear operator equations under restrictive assumptions. The sufficient conditions for approximate controllability are derived under the natural assumptions on the nonlinear terms, which is an odd homogeneous and the nonlinear inverse considered as a multivalued mapping is bounded. An example is given to illustrate our main results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
173. Model predictive guidance for active aircraft protection from a homing missile.
- Author
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Shi, Heng, Chen, Zheng, Zhu, Jihong, and Kuang, Minchi
- Subjects
PREDICTIVE control systems ,PREDICTION models ,FIXED point theory ,NONLINEAR operators ,ITERATIVE methods (Mathematics) - Abstract
This paper proposes a novel guidance law based on model predictive control for protecting an aircraft from a homing missile. Considering that in the target‐missile‐defender engagement the attacking missile is pursuing the target aircraft by employing a known linear guidance law, a non‐linear predictive model for the engagement is established. This predictive model allows converting the three‐body engagement to a one‐on‐one engagement. The time‐to‐go for the defender towards the future position of the incoming missile is analytically derived, indicating that the optimal time for the defender to intercept the incoming missile is a fixed‐point of a real‐valued function. As a result, the optimal interception duration can be obtained by a standard fixed‐point iteration method, and thus the interception point can be readily predicted via integrating the predictive model. The guidance command is generated by directly leading the defender to the predicted intercept point. Numerical simulations in different scenarios validate the algorithm to be computationally efficient, and demonstrate that the proposed strategy outperforms previous techniques in terms of miss distance, engagement duration, and the control effort. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
174. Asymptotic behavior for nonlinear degenerate parabolic equations with irregular data.
- Author
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Niu, Weisheng, Meng, Qing, and Chai, Xiaojuan
- Subjects
DEGENERATE parabolic equations ,NONLINEAR operators - Abstract
This paper focuses on the following degenerate parabolic equation u t − d i v (σ (x) | ∇ u | p − 2 ∇ u) + f (x , u) = g i n Ω × R + , u = 0 o n ∂ Ω × R + , u (x , 0) = u 0 (x) i n Ω , where Ω is a smooth bounded domain in R N , (N ≥ 2) , 1 < p < N , u 0 , g ∈ L 1 (Ω) , σ (x) is positive almost everywhere and satisfies proper degenerate conditions. The existence and uniqueness result is proved in the framework of entropy solutions. For the long-time behavior, we prove the existence of a global attractor in L q (Ω) by using some delicate estimates on the solution, which are derived by taking advantage of both the leading operator and the zero-order nonlinear term. The aforementioned results improve some previous results in the literature in several aspects. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
175. Symmetric Properties for Choquard Equations Involving Fully Nonlinear Nonlocal Operators.
- Author
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Wang, Pengyan, Chen, Li, and Niu, Pengcheng
- Subjects
NONLINEAR operators ,EQUATIONS ,INFINITY (Mathematics) - Abstract
In this paper we consider the following nonlinear nonlocal Choquard equation F α u (x) + ω u (x) = C n , 2 s | x | 2 s - n ∗ u q (x) u r (x) , x ∈ R n , where 0 < s < 1 , 0 < α < 2 , F α is the fully nonlinear nonlocal operator: F α (u (x)) = C n , α P. V. ∫ R n F (u (x) - u (y)) x - y n + α d y. The positive solution to nonlinear nonlocal Choquard equation is shown to be symmetric and monotone by using the moving plane method which has been introduced by Chen, Li and Li in 2015. We first turn single equation into equivalent system of equations. Then the key ingredients are to obtain the "narrow region principle" and "decay at infinity" for the corresponding problems. We also get radial symmetry results of positive solution for the Schrödinger-Maxwell nonlocal equation. Similar ideas can be easily applied to various nonlocal problems with more general nonlinearities. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
176. Optimal Control of a Class of Variational–Hemivariational Inequalities in Reflexive Banach Spaces.
- Author
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Sofonea, Mircea
- Subjects
BANACH spaces ,CONVEX sets ,MATHEMATICAL equivalence ,NONLINEAR operators ,OPTIMAL control theory ,FUNCTIONALS ,MATHEMATICAL models - Abstract
The present paper represents a continuation of Migórski et al. (J Elast 127:151–178, 2017). There, the analysis of a new class of elliptic variational–hemivariational inequalities in reflexive Banach spaces, including existence and convergence results, was provided. An inequality in the class is governed by a nonlinear operator, a convex set of constraints and two nondifferentiable functionals, among which at least one is convex. In the current paper we complete this study with new results, including a convergence result with respect the set of constraints. Then we formulate two optimal control problems for which we prove the existence of optimal pairs, together with some convergence results. Finally, we exemplify our results in the study of a one-dimensional mathematical model which describes the equilibrium of an elastic rod in unilateral contact with a foundation, under the action of a body force. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
177. Noncoercive mixed equilibrium problems under pseudomonotone perturbations and applications to nonlinear evolution equations with lack of coercivity.
- Author
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Al-Homidan, Suliman, Ansari, Qamrul Hasan, and Chadli, Ouayl
- Subjects
NONLINEAR evolution equations ,NONLINEAR operators ,COERCIVE fields (Electronics) ,EQUILIBRIUM ,MONOTONE operators - Abstract
In this paper, we study the existence of solutions for noncoercive mixed equilibrium problems which are described by the sum of a maximal monotone bifunction and a pseudomonotone (or quasimonotone) bifunction in the sense of Brézis. Our approach is based on recession analysis and on recent results established by the authors for the existence of solutions of mixed equilibrium problems under pseudomonotone perturbations. As an application, we study the existence of solutions for nonlinear evolution equations associated with a noncoercive time-dependent pseudomonotone (or quasimonotone) operator. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
178. A new fuzzy sliding mode controller design for delta operator time-delay nonlinear systems.
- Author
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Ji, Wenqiang, Ma, Min, and Qiu, Jianbin
- Subjects
NONLINEAR systems ,TIME delay systems ,SLIDING mode control ,NONLINEAR operators ,LINEAR matrix inequalities ,CLOSED loop systems ,MOTION analysis - Abstract
This paper investigates the sliding mode control (SMC) problem for a class of delta operator uncertain time-delay nonlinear systems through Takagi–Sugeno fuzzy models. Some new sufficient conditions for asymptotic stability analysis of the sliding motion are obtained in terms of linear matrix inequalities with some convexification techniques. Then two new dynamic SMC design methods are synthesised to force the resulting closed-loop system states onto the sliding surface in finite time. Two simulation examples are finally given to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
179. Control problems for semi-linear retarded integro-differential equations by the Fredholm theory.
- Author
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Kang, Yong Han and Jeong, Jin-Mun
- Subjects
FREDHOLM equations ,INTEGRO-differential equations ,INTERPOLATION spaces ,FUNCTIONAL equations ,NONLINEAR operators ,NONLINEAR functional analysis - Abstract
In this paper, we deal with the approximate controllability for semi-linear retarded functional integro-differential equations by using the Fredholm theory in Hilbert spaces. We no longer require the compactness of structural operators to obtain the approximate controllability for the nonlinear differential system, but instead we use the theory of interpolation spaces and the regularity of solutions of semi-linear given equations with unbounded principal operators. Finally, based on the properties of general degree theory in infinite dimensional spaces, we investigate the relation between the reachable set of trajectories of the semi-linear retarded functional integro-differential system and that of its corresponding linear system excluded by the nonlinear term. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
180. INEXACT NEWTON'S METHOD FOR GENERALIZED OPERATOR EQUATIONS IN BANACH SPACES.
- Author
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Singh, Vipin Kumar
- Subjects
OPERATOR equations ,NEWTON-Raphson method ,BANACH spaces ,NONLINEAR operators - Abstract
In the present paper, we introduce a new inexact Newton-like algorithm for solving the generalized operator equations containing non differentiable operators in Banach space setting and discuss its semilocal convergence analysis under the weak Lipschitz condition with larger convergence domain and tighter error bounds. The main result of this paper is the significant improvement over the Newton's method as well as the inexact Newton method. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
181. Preface: Special issue on approximation by linear and nonlinear operators with applications. Part I.
- Author
-
Costarelli, Danilo
- Subjects
NONLINEAR operators ,APPROXIMATION theory ,APPLIED mathematics ,LINEAR operators ,MATHEMATICAL analysis ,HARMONIC analysis (Mathematics) - Published
- 2021
- Full Text
- View/download PDF
182. Re: Comment on “New methods for old Coulomb few-body problems”.
- Author
-
Harris, Frank E., Frolov, Alexei M., and Smith, Vedene H.
- Subjects
ELECTRIC fields ,POTENTIAL theory (Physics) ,INTEGRALS ,INVARIANTS (Mathematics) ,NONLINEAR operators ,QUANTUM chemistry - Abstract
The scope and purpose of the subject paper by the present authors
Int J Quantum Chem 2004, 100, 1086 are clarified. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [ABSTRACT FROM AUTHOR]- Published
- 2006
- Full Text
- View/download PDF
183. The majorant function modelling to solve nonlinear algebraic system.
- Author
-
Hameed, Hameed Husam and Al-Saedi, Hayder M.
- Subjects
- *
NONLINEAR systems , *NONLINEAR operators , *OPERATOR equations , *JACOBIAN matrices , *MATRIX inversion - Abstract
The majorize modelling of the modified Newton method (MNM) is an effective tool for concluding the existence and uniqueness of the solution of nonlinear operator equations. In this paper, we consider MNM together with a new majorant function (MF) that needed weak conditions to solve a nonlinear algebraic system (NLAS). The main advantage of this method is that you only require to establish the inverse of the Jacobian matrix (JM) at the initial guess (IG) and there is no need to compute it at the other iterations. The proposed strategy in this paper is logical and easy to execute. The theorems of MF and convergence are established for the method. Numerical results show that the strategy is efficient and promising. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
184. STABILITY OF NONAUTONOMOUS IMPULSIVE EVOLUTION SYSTEM ON TIME SCALE.
- Author
-
ZADA, AKBAR, ARAFAT, YASIR, and SHAH, SYED OMAR
- Subjects
FIXED point theory ,EQUALITY ,NONLINEAR operators ,DYNAMICAL systems ,NORMAL operators - Abstract
The main theme of this article is to discuss the existence, uniqueness and β -Ulam type stability for nonautonamous impulsive differential systems on time scale by applying fixed point method. The major components to proof the results are the Grönwall inequality on time scale, abstract Grönwall lemma and Picard operator. Some suppositions are made for achieving our results. At last, the main result is validated by the example specified in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
185. On Lyapunov-type inequalities for (n + 1)st order nonlinear differential equations with the antiperiodic boundary conditions.
- Author
-
AKTAŞ, Mustafa Fahri
- Subjects
BOUNDARY value problems ,NONLINEAR differential equations ,NONLINEAR operators - Abstract
In this paper, we establish new Lyapunov-type inequalities for (n + 1)st order nonlinear differential equation including p-relativistic operator and q -prescribed curvature operator under the antiperiodic boundary conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
186. Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional p-Laplacian.
- Author
-
Zhang, Lihong, Hou, Wenwen, Ahmad, Bashir, and Wang, Guotao
- Subjects
SYMMETRY ,MULTISCALE modeling ,EQUATIONS ,INFINITY (Mathematics) ,LAPLACIAN operator ,NONLINEAR operators - Abstract
In this paper, we investigate radial symmetry and monotonicity of positive solutions to a logarithmic Choquard equation involving a generalized nonlinear tempered fractional p-Laplacian operator by applying the direct method of moving planes. We first introduce a new kind of tempered fractional p-Laplacian (− Δ − λ
ƒ )s p based on tempered fractional Laplacian (Δ + λ)β/2 , which was originally defined in [ 3 ] by Deng et.al [Boundary problems for the fractional and tempered fractional operators, Multiscale Model. Simul., 16(1)(2018), 125-149]. Then we discuss the decay of solutions at infinity and narrow region principle, which play a key role in obtaining the main result by the process of moving planes. [ABSTRACT FROM AUTHOR]- Published
- 2021
- Full Text
- View/download PDF
187. Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator.
- Author
-
Yang, Zedong, Wang, Guotao, Agarwal, Ravi P., and Xu, Haiyong
- Subjects
NONLINEAR operators ,NONLINEAR systems ,POSITIVE systems ,SEMILINEAR elliptic equations - Abstract
In this paper, we study the positive solutions of the Schrödinger elliptic system { div(G(|∇y|
p−2 )∇y) = b1 (|x|)ψ(y) + h1 (|x|)φ(z), x ∈ Rn (n ≥ 3), div (G(|∇z|p−2 )∇z) = b2 (|x|)ψ(z) + h2 (|x|)φ(y), x ∈ Rn , where G is a nonlinear operator. By using the monotone iterative technique and Arzela-Ascoli theorem, we prove that the system has the positive entire bounded radial solutions. Then, we establish the results for the existence and nonexistence of the positive entire blow-up radial solutions for the nonlinear Schrödinger elliptic system involving a nonlinear operator. Finally, three examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]- Published
- 2021
- Full Text
- View/download PDF
188. Galerkin finite element method for nonlinear fractional differential equations.
- Author
-
Nedaiasl, Khadijeh and Dehbozorgi, Raziyeh
- Subjects
NONLINEAR differential equations ,NONLINEAR boundary value problems ,FINITE element method ,CAPUTO fractional derivatives ,DIFFERENTIAL operators ,FRACTIONAL differential equations - Abstract
In this paper, we study the existence, regularity, and approximation of the solution for a class of nonlinear fractional differential equations. In order to do this, suitable variational formulations are defined for nonlinear boundary value problems with Riemann-Liouville and Caputo fractional derivatives together with the homogeneous Dirichlet condition. We investigate the well-posedness and also the regularity of the corresponding weak solutions. Then, we develop a Galerkin finite element approach for the numerical approximation of the weak formulations and drive a priori error estimates and prove the stability of the schemes. Finally, some numerical experiments are provided to demonstrate the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
189. Positive solutions to nonlinear first-order impulsive dynamic equations on time scales.
- Author
-
Guan, Wen
- Subjects
FIXED point theory ,BOUNDARY value problems ,IMPULSIVE differential equations ,NONLINEAR equations ,NONLINEAR operators - Abstract
By using the classical fixed point theorem for operators on a cone, in this paper, some results of single and multiple positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. It is worth noticing that the nonlinearity f and the pulse function in this paper are not positive. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
190. Biogeography Based optimization with Salp Swarm optimizer inspired operator for solving non-linear continuous optimization problems.
- Author
-
Garg, Vanita, Deep, Kusum, Alnowibet, Khalid Abdulaziz, Zawbaa, Hossam M., and Mohamed, Ali Wagdy
- Subjects
NONLINEAR operators ,BIOGEOGRAPHY - Abstract
In this paper, a novel attempt is made to incorporate the two effective algorithm strategies, where BBO has a strong exploration and Salp Swarm Algorithm (SSA) is used for exploitation of the search space. The proposed algorithm is tested on IEEE CEC 2014 and statistical, convergence graphs are given. The proposed algorithm is also applied to 10 real life problems and compared with its counterpart algorithm. Results obtained by above experiments have demonstrated the outperformance of the hybrid version of BBO over other algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
191. Basis operator network: A neural network-based model for learning nonlinear operators via neural basis.
- Author
-
Hua, Ning and Lu, Wenlian
- Subjects
- *
NONLINEAR operators , *FUNCTION spaces - Abstract
It is widely acknowledged that neural networks can approximate any continuous (even measurable) functions between finite-dimensional Euclidean spaces to arbitrary accuracy. Recently, the use of neural networks has started emerging in infinite-dimensional settings. Universal approximation theorems of operators guarantee that neural networks can learn mappings between infinite-dimensional spaces. In this paper, we propose a neural network-based method (BasisONet) capable of approximating mappings between function spaces. To reduce the dimension of an infinite-dimensional space, we propose a novel function autoencoder that can compress the function data. Our model can predict the output function at any resolution using the corresponding input data at any resolution once trained. Numerical experiments demonstrate that the performance of our model is competitive with existing methods on the benchmarks, and our model can address the data on a complex geometry with high precision. We further analyze some notable characteristics of our model based on the numerical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
192. σ-CENTRALIZERS OF GENERALIZED MATRIX ALGEBRAS.
- Author
-
ASHRAF, MOHAMMAD and ANSARI, MOHAMMAD AFAJAL
- Subjects
- *
MATHEMATICS , *FIXED point theory , *NONLINEAR operators , *INTEGRO-differential equations , *DERIVATIVES (Mathematics) - Abstract
In the present paper, we characterize Lie (Jordan) σ-centralizers of generalized matrix algebras. More precisely, we obtain some conditions under which every Lie σ-centralizer of a generalized matrix algebra can be expressed as the sum of a σ-centralizer and a center- valued mapping. Further, it is shown that under certain appropriate assumptions every Jordan σ-centralizer of a generalized matrix algebra is a σ-centralizer. Finally, the main results are applied to triangular algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
193. ON THE COMPARISON OF THE MARCINKIEWICZ AND LUXEMBURG NORMS OF THE EXPONENTIAL SPACE.
- Author
-
MEZŐ, ISTVÁN
- Subjects
- *
MATHEMATICS , *FIXED point theory , *NONLINEAR operators , *INTEGRO-differential equations , *DERIVATIVES (Mathematics) - Abstract
The exponential space, which is a Banach function space, can be defined with two very differently looking, but equivalent norms. In this paper, we give estimates for the best constants of the ratio of these two norms. Our result answers a question of C. Bennett, and R. Sharpley. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
194. TOLERANCES ON POSETS.
- Author
-
CHAJDA, IVAN and LÄNGER, HELMUT
- Subjects
- *
MATHEMATICS , *FIXED point theory , *NONLINEAR operators , *INTEGRO-differential equations , *DERIVATIVES (Mathematics) - Abstract
The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventies of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Czédli ([7]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radeleczki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
195. QUALITATIVE STUDY FOR IMPULSIVE PANTOGRAPH FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION VIA ψ-HILFER DERIVATIVE.
- Author
-
BEDDANI, MOUSTAFA, BEDDANI, HAMID, and FEČKAN, MICHAL
- Subjects
- *
MATHEMATICS , *FIXED point theory , *NONLINEAR operators , *INTEGRO-differential equations , *DERIVATIVES (Mathematics) - Abstract
In this paper, we study the existence and stability of solutions for impulsive pantograph fractional integro-differential equation via ψ-Hilfer fractional derivative in a appropriate Banach space. Our approach is based on fixed point theorems of Darbo’s and Mönch via Kuratowski measure of non-compactness. An example is given to illustrate our approach. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
196. Fully nonlinear free transmission problems.
- Author
-
Pimentel, Edgard A. and Santos, Makson S.
- Subjects
NONLINEAR operators ,ELLIPTIC operators ,VISCOSITY - Abstract
We examine a free transmission problem driven by fully nonlinear elliptic operators. Since the transmission interface is determined endogenously, our analysis regards this object as a free boundary. We start by relating our problem with a pair of viscosity inequalities. Then, approximation methods ensure that strong solutions are of class C 1;Log-Lip, locally. In addition, under further conditions on the problem, we prove quadratic growth of the solutions away from branch points. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
197. Fixed Point, Data Dependence, and Well-Posed Problems for Multivalued Nonlinear Contractions.
- Author
-
Iqbal, Iram, Hussain, Nawab, Al-Sulami, Hamed H., and Hassan, Shanza
- Subjects
NONLINEAR equations ,NONLINEAR operators ,METRIC spaces ,CONTRACTIONS (Topology) - Abstract
The aim of the paper is to discuss data dependence, existence of fixed points, strict fixed points, and well posedness of some multivalued generalized contractions in the setting of complete metric spaces. Using auxiliary functions, we introduce Wardowski type multivalued nonlinear operators that satisfy a novel class of contractive requirements. Furthermore, the existence and data dependence findings for these multivalued operators are obtained. A nontrivial example is also provided to support the results. The results generalize, improve, and extend existing results in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
198. A dividend optimization problem with constraint of survival probability in a Markovian environment model.
- Author
-
Tan, Jiyang and Yuan, Senlin
- Subjects
NONLINEAR operators ,DIVIDENDS ,RANDOM variables ,ALGORITHMS ,METRIC spaces ,PROBABILITY theory ,MARKOV processes - Abstract
In this paper, the optimal dividend problem in a discrete-time risk model with interest is discussed. Assume that the premium received per unit time is a positive real-valued random variable, and the sequence of premiums is a Markov chain owing to the environmental effects. In arbitrary unit time whether a claim occurs or not is related to the premium received in the corresponding period. Under the constraint of a given survival probability, the optimal control strategy for dividends paid periodically to the shareholders is considered. We provide some properties and an algorithm for the optimal control strategy by structuring a non-linear operator and applying the fixed point theorem. Numerical examples are presented to illustrate the algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
199. FIXED POINT THEOREM AND SELF-SIMILARITY ON MIXED VICSEK PATTERNS.
- Author
-
SIMON, LEVENTE
- Subjects
- *
FIXED point theory , *NONLINEAR operators , *SIMILARITY (Geometry) , *FRACTAL analysis , *GEOMETRIC shapes - Abstract
The purpose if this paper is to present a fixed point result constructed by finite sequences. Using iterated function systems and related fractal operators, a mixed patterns generated by the a finite sequence patterns construct the sets of patterns built by black and white squares. A complete metric space related to a mixed pattern sequence is defined using the distance based on difference of the black squares' area. The main result of the paper highlights that these fractal operators has unique fixed points for the sets generated by the mixed patterns. Moreover, the main theorem is also applied for Vicsek fractals such that results also hold for mixed Vicsek patterns. Motivated by various studies on growing graph sequences and related large structures, this paper underlines a new connection between fixed point theory and network science. Using circle patterns, the paper also interprets the main result on sets mixed patterns based on touching circles. Thus, the paper focuses a fixed point theorem on the sets mixed patterns built by iterated function systems and the distances calculated between the areas of these geometric shapes. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
200. SOLVABILITY OF CONTROL PROBLEM FOR A NONLOCAL NEUTRAL STOCHASTIC FRACTIONAL INTEGRO-DIFFERENTIAL INCLUSION WITH IMPULSES.
- Author
-
CHADHA, ALKA and BORA, SWAROOP NANDAN
- Subjects
HILBERT'S tenth problem ,HILBERT space ,FRACTIONAL calculus ,FIXED point theory ,NONLINEAR operators - Abstract
This paper considers a class of neutral impulsive stochastic integro-differential inclusion with nonlocal conditions involving the Caputo fractional derivative of order 1 < α< 2 in a Hilbert space. A new set of sufficient conditions for the approximate controllability of semilinear fractional stochastic systems is derived utilizing solution operator, stochastic analysis, fractional calculus and fixed point theorem for a multivalued operator under the assumption that the corresponding linear system is approximately controllable. An example is provided to illustrate the derived theory at the end of the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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