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The object of this paper was to study two majorization results for the subclasses S s ∗ and S c ∗ of starlike functions, which are, respectively, associated with the sine and cosine functions, without acting upon any linear or nonlinear operators to the above function classes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of square-mean piecewise almost automorphic function. By using the theory of semigroups of operators and the contraction mapping principle, the existence of square-mean piecewise almost automorphic mild solutions for linear and nonlinear impulsive stochastic evolution equations is investigated. In addition, the exponential stability of square-mean piecewise almost automorphic mild solutions for nonlinear impulsive stochastic evolution equations is obtained by the generalized Gronwall–Bellman inequality. Finally, we provide an illustrative example to justify the results. [ABSTRACT FROM AUTHOR]

In this paper, a normal S-iterative algorithm is studied and analyzed for solving a general class of variational inequalities involving a set of fixed points of nonexpansive mappings and two nonlinear operators. It is shown that the proposed algorithm converges strongly under mild conditions. The rate of convergence of the proposed iterative algorithm is also studied. An equivalence of convergence between the normal S-iterative algorithm and Algorithm 2.6 of Noor (J. Math. Anal. Appl. 331, 810–822, 2007) is established and a comparison between the two is also discussed. As an application, a modified algorithm is employed to solve convex minimization problems. Numerical examples are given to validate the theoretical findings. The results obtained herein improve and complement the corresponding results in Noor (J. Math. Anal. Appl. 331, 810–822, 2007). [ABSTRACT FROM AUTHOR]

In the present paper, we establish some fixed-point theorems for a 2 × 2 block operator matrix involving multivalued maps acting on Banach spaces. These results are formulated in terms of weak sequential continuity and the technique of measures of weak noncompactness. The results obtained are then applied to a coupled system of nonlinear equations. [ABSTRACT FROM AUTHOR]

The paper provides results of the study of correctness of the mathematical model that includes the influence of stresses on irradiation-induced swelling of metal in the problems of elastic-plastic deformation mechanics. The present-day approaches to modeling irradiation-induced swelling, which take into account a damaging dose, irradiation temperature, and the effect of the stress state on the swelling deformation, are discussed. The constitutive equations that describe the elasticplastic deformation processes allowing for the influence of a stress mode on the irradiation-induced swelling in metal are put forward. Analysis of these equations has made it possible to find the conditions that ensure correctness of the plasticity equations considered and to make a lower-bound estimate of the maximum permissible value of free swelling and irradiation dose. A priori estimates of the maximum permissible value of free swelling and damaging dose are given for 08Kh18N10T steel under various irradiation temperatures. In the practice of strength design such estimates are needed at the stage of problem formulation in order to analyze adequacy of input data, for they enable one to assess a prior the possibility of solving the problem for a given temperature and irradiation dose. The boundary-value problem that describes non-isothermal processes of elasticplastic deformation including swelling strains has been defined in the form of a nonlinear operator equation. Based on the findings regarding the correctness of the constitutive equations, we have established the existence and uniqueness of the generalized solution and its continuous dependence on applied loads, thermal strains and swelling strains. The convergence of the method of elasticity solutions and the method of variable elasticity parameters has been studied as applied to a thermoplasticity problem including irradiation-induced swelling strains. [ABSTRACT FROM AUTHOR]

This paper is concerned with the differential sensitivity analysis of variational inequalities in Banach spaces whose solution operators satisfy a generalized Lipschitz condition. We prove a sufficient criterion for the directional differentiability of the solution map that turns out to be also necessary for elliptic variational inequalities in Hilbert spaces (even in the presence of asymmetric bilinear forms, nonlinear operators and nonconvex functionals). Our method of proof is fully elementary. Moreover, our technique allows us to also study those cases where the variational inequality at hand is not uniquely solvable and where directional differentiability can only be obtained w.r.t. the weak or the weak-star topology of the underlying space. As tangible examples, we consider a variational inequality arising in elastoplasticity, the projection onto prox-regular sets, and a bang–bang optimal control problem. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of a non‐autonomous porous elastic systems with nonlinear damping and sources terms. By employing nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions. We also prove the existence of minimal pullback attractors with respect to a universe of tempered sets defined by the sources terms. Finally, we prove the upper‐semicontinuity of pullback attractors with respect to non‐autonomous perturbations. [ABSTRACT FROM AUTHOR]

Increasing attention is paid to modeling flexibility of individual components in the multibody simulation of large-scale mechanical systems. Nevertheless, the high model order of common methods such as FEA restricts efficient explorations, especially in dynamic design and iterative optimization. In this paper, a rigid multibody modeling strategy (RMMS) with low DOFs and explicit physical meaning is proposed, which directly discretizes a continuous structure into a number of rigid finite elements (RFEs) connected by spring-damping elements (SDEs). In the RMMS, a new identification method from the perspective of the inverse vibration problem is particularly put forward to resolve the parameters of SDEs, which is crucial to the implementation of RMMS in complex flexible structures. With decoupling and linearization, this nonlinear problem is transformed into solving the incompatible linear equations in R n 2 vector space based on vectorization operator and Kronecker product, and optimal parameters are obtained by calculating the Moore–Penrose generalized inverse. Finally, the comparison of the experimental results with the simulated ones by the RMMS strongly validates the feasibility and correctness of the RMMS in predicting the dynamic behaviors while with few DOFs and explicit physical meaning; the application in a lithography system exhibits the applicability of the RMMS for dynamic modeling of large-scale mechanical systems. [ABSTRACT FROM AUTHOR]

Many iterative algorithms like Picard, Mann, Ishikawa are very useful to solve fixed point problems of nonlinear operators in real Hilbert spaces. The recent trend is to enhance their convergence rate abruptly by using inertial terms. The purpose of this paper is to investigate a new inertial iterative algorithm for finding the fixed points of nonexpansive operators in the framework of Hilbert spaces. We study the weak convergence of the proposed algorithm under mild assumptions. We apply our algorithm to design a new accelerated proximal gradient method. This new proximal gradient technique is applied to regression problems. Numerical experiments have been conducted for regression problems with several publicly available high-dimensional datasets and compare the proposed algorithm with already existing algorithms on the basis of their performance for accuracy and objective function values. Results show that the performance of our proposed algorithm overreaches the other algorithms, while keeping the iteration parameters unchanged. [ABSTRACT FROM AUTHOR]

In this paper we design a family of cell-average nonlinear prediction operators that make use of the generalized harmonic means and we apply the resulting schemes to image processing. The new family of nonlinear schemes conserve the numerical properties of the linear schemes, such as the L 1 -stability, the order of accuracy or compression rate but avoiding Gibbs phenomenon close to the discontinuities. The generalized harmonic mean was introduced in the framework of point-values in [A. Guessab, M. Moncayo, and G. Schmeisser, A class of nonlinear four-point subdivision schemes. Properties in terms of conditions, Adv. Comput. Math. 37 (2012), pp. 151–190] in order to improve the results of the harmonic mean. However, in the cell-average setting our conclusion is that, from a numerical point of view, the advantage of using the new mean is not clear. [ABSTRACT FROM AUTHOR]

It is our purpose in this paper to prove some fixed point results and Fejer monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type Volterra-Fredholm functional nonlinear integral equation in complex valued Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, a general fixed point theorem for quasi-contractions in b-metric spaces, which is a sharp improvement of Amini-Harandi's result, Mitrovic and Hussain's result, and is a generalization of many b-metric fixed point theorems in the literature, is proved. The technique overcomes some limits in b-metric fixed point theory compared to metric fixed point theory. The obtained results are also supported by examples. [ABSTRACT FROM AUTHOR]

This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We show order optimal rates of convergence for finitely smoothing operators and for the backwards heat equation for a range of Besov spaces using variational source conditions. We also derive order optimal rates for a white noise model with the help of variational source conditions and concentration inequalities for sharp negative Besov norms of the noise. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of common fixed point for three mappings in Gb-complete Gb-metric space. On the other hand, we prove that the theory is also established in G-metric space and several corollaries and examples are listed. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions for the nonlinear p(.) degenerate problems involving nonlinear operators of the form - div a(x, ∇u) = f(x, u, ∇u) where a and fare Caratheodoryfunctions satisfying some nonstandard growth conditions. [ABSTRACT FROM AUTHOR]

In this paper we investigate the stability and asymptotic stability of the zero solution for the first order delay differential equation þ(t)=-ΣNj=1(t)y(t-τj(t))+f(t,y(t-964;(t)) where the delay is variable and by using Banach fixed point theorem. We give new conditions to ensure the stability and asymptotic stability of the zero solution of this equation. [ABSTRACT FROM AUTHOR]

This paper is devoted to the algorithm of the linear Cauchy problem solution for large systems of first-order ordinary differential equations using parallel calculations. The proof of the convergence of the iteration process using the solution as expansion over orthogonal polynomials for the interval [0,1] is presented. The features of this algorithm are its simplicity, the opportunity to get a solution by parallel calculations, and also the possibility to get a solution for nonlinear problems by changing the operator using the solution from the iteration process. [ABSTRACT FROM AUTHOR]

In this paper, we study the relationship between the class of weakly demicompact linear operators, introduced in [KRICHEN, B.—O'REGAN, D.: On the class of relatively weakly demicompact nonlinear operators, Fixed Point Theory 19 (2018), 625–630], and measures of weak noncompactness of linear operators with respect to an axiomatic one. Moreover, some Fredholm and perturbation results involving the class of weakly demicompact linear operators are investigated. Our results are then used to investigate the relationship between the relative essential spectrum of the sum of two linear operators and the relative essential spectrum of each of these operators. [ABSTRACT FROM AUTHOR]

In this paper, we consider a family of nonlinear integral operators of Urysohn‐type and study the pointwise convergence of the family at characteristic points of L1−function. The kernel Kλ(x,t,u(t)) depends on the positive parameter λ changing on the set of numbers with the accumulation point at infinity and Kλ(x,t,u(t)) is an entire analytic function of variable u, which is a bounded function belonging to L1(R). [ABSTRACT FROM AUTHOR]

In this paper, we establish global Sobolev a priori estimates for L p -viscosity solutions of fully nonlinear elliptic equations as follows: F (D 2 u , D u , u , x) = f (x) in  Ω u (x) = φ (x) on  ∂ Ω by considering minimal integrability condition on the data, i.e. f ∈ L p (Ω) , φ ∈ W 2 , p (Ω) for n < p < ∞ and a regular domain Ω ⊂ ℝ n , and relaxed structural assumptions (weaker than convexity) on the governing operator. Our approach makes use of techniques from geometric tangential analysis, which consists in transporting "fine" regularity estimates from a limiting operator, the Recession profile, associated to F to the original operator via compactness methods. We devote special attention to the borderline case, i.e. when f ∈ p − BMO ⊋ L ∞ . In such a scenery, we show that solutions admit BMO type estimates for their second derivatives. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of local stable manifolds for a semi-linear differential equation, where the linear part is a Hille–Yosida operator on a Banach space and the nonlinear forcing term f satisfies the φ -Lipschitz conditions, where φ belongs to certain classes of admissible function spaces. The approach being used is the fixed point arguments and the characterization of the exponential dichotomy of evolution equations in admissible spaces of functions defined on the positive half-line. [ABSTRACT FROM AUTHOR]

In this paper, we study the first eigenvalue of a nonlinear elliptic system involving p -Laplacian as the differential operator. The principal eigenvalue of the system and the corresponding eigenfunction are investigated both analytically and numerically. An alternative proof to show the simplicity of the first eigenvalue is given. In addition, an upper and lower bounds of the first eigenvalue are provided. Then, a numerical algorithm is developed to approximate the principal eigenvalue. This algorithm generates a decreasing sequence of positive numbers and various examples numerically indicate its convergence. Further, the algorithm is generalized to a class of gradient quasilinear elliptic systems. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop analytic techniques to deal with Hankel-total positivity of sequences. We show two nonlinear operators preserving Stieltjes moment property of sequences. They actually both extend a result of Wang and Zhu that if (an)n≥0 is a Stieltjes moment sequence, then so is (an+2an - a²n+1)n≥0. Using complete monotonicity of functions, we also prove Stieltjes moment properties of the sequences ...and .... Particularly in a new unified manner our results imply the Stieltjes moment properties of binomial coefficients (pn+r-1 n) and Fuss- Catalan numbers r/pn+r (pn+r n) proved by Mlotkowski, Penson, and Zyczkowski, and Liu and Pego, respectively, and also extend some results for log-convexity of sequences proved by Chen-Guo-Wang, Su-Wang, Yu, and Wang-Zhu, respectively. [ABSTRACT FROM AUTHOR]

In this paper an improved version of a verification algorithm for solving nonlinear systems of equations based on Krawczyk operator is presented. Compared with the original algorithm, the improved verification algorithm not only saves computing time, but also computes a narrower (or at least the same) inclusion of the solution to nonlinear systems of equations for certain classes of problems. Numerical results demonstrate the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper we obtain symmetry and monotonicity of positive solutions for the systems involving fully nonlinear nonlocal operators in a domain (bounded or unbounded) in R n via using a direct method of moving planes. This extends the results in Wang and Niu (2017) and also is the first result of the symmetry for a fully nonlinear nonlocal system containing gradient terms with different order. [ABSTRACT FROM AUTHOR]

In this paper we first introduce N̅qΔ − summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrix A to map these sequence spaces on the spaces c, c0 and l∞. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces. [ABSTRACT FROM AUTHOR]

Let U be a Hilbert A-module and L(U) the set of all adjointable A-linear maps on U. Let K = {Λx ∈ L(U, Vx) : x ∈ X } and L = {Γx ∈ L(U, Vx) : x ∈ X } be two continuous g-frames for U, K is said to be similar with L if there exists an invertible operator J ∈ L(U) such that Γx = ΛxJ, for all x ∈ X . In this paper, we define the concepts of closeness and nearness between two continuous g-frames. In particular, we show that K and L are near, if and only if they are similar. [ABSTRACT FROM AUTHOR]

A nonlinear Markov chain is a discrete time stochastic process whose transitions may depend on both the current state and the current distribution of the process. The nonlinear Markov chain over a finite state space can be identified by a continuous mapping (the so-called nonlinear Markov operator) defined on a set of all probability distributions (which is a simplex) of the finite state space and by a family of transition matrices depending on occupation probability distributions of states. In this paper, we introduce a notion of Dobrushin's ergodicity coefficients for stochastic hypermatrices and provide a criterion for the contraction nonlinear Markov operator by means of Dobrushin's ergodicity coefficients. We also introduce a notion of p − majorizing nonlinear Markov operators associated with stochastic hypermatrices and provide a criterion for strong ergodicity of such kind of operator. We show that the p − majorizing nonlinear Markov operators associated with scrambling , Sarymsakov , and Wolfowitz stochastic hypermatrices are strongly ergodic. These classes of p − majorizing nonlinear Markov operators assure an existence of a residual set of strongly ergodic nonlinear Markov operators which are not contractions. Some supporting examples are also provided. [ABSTRACT FROM AUTHOR]

We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations ∂tu-Lσ,μ[φ(u)] = f in RN×(0,T), where Lσ,μ is a general symmetric diffusion operator of Lévy type and φ is merely continuous and non-decreasing. We then use this theory to prove convergence for many different numerical schemes. In the nonlocal case most of the results are completely new. Our theory covers strongly degenerate Stefan problems, the full range of porous medium equations, and for the first time for nonlocal problems, also fast diffusion equations. Examples of diffusion operators Lσ,μ are the (fractional) Laplacians Δ and -(-Δ)α/2 for α ∈ (0,2), discrete operators, and combinations. The observation that monotone finite difference operators are nonlocal Lévy operators, allows us to give a unified and compact nonlocal theory for both local and nonlocal, linear and nonlinear diffusion equations. The theory includes stability, compactness, and convergence of the methods under minimal assumptions, including assumptions that lead to very irregular solutions. As a byproduct, we prove the new and general existence result announced in [F. del Teso, J. Endal, and E. R. Jakobsen, C. R. Math. Acad. Sci. Paris, 355 (2017), pp. 1154--1160]. We also present some numerical tests, but extensive testing is deferred to the companion paper [F. del Teso, J. Endal, and E. R. Jakobsen, SIAM J. Numer. Anal., 56 (2018), pp. 3611-3647] along with a more detailed discussion of the numerical methods included in our theory. [ABSTRACT FROM AUTHOR]

In this paper we consider optimal feedback control problems for a general class of nonlinear partially observed stochastic evolution equations on Banach spaces. The system is governed by a pair of (coupled) stochastic evolution equations, one representing the main system and the other representing the observer. Both are governed by stochastic evolution equations on unconditional Martingale difference Banach spaces. The state of the second system, which is observable, is used to provide the input to control the main system. We present the existence of mild solutions of the system equations and then introduce a class of admissible nonlinear feedback operators. The space of feedback operators is endowed with the topology of pointwise convergence on the domain space with respect to the weak topology in the range space giving a compact Hausdorff space. This is then used to prove the existence of an optimal output feedback control law for the Bolza problem. Also we prove the weak compactness of the attainable set of induced measures and prove the existence of optimal feedback control laws for several nontypical control problems involving measures. [ABSTRACT FROM AUTHOR]

Let Ω be a bounded open set of R n , n ≥ 2. In this paper we mainly study some properties of the second Dirichlet eigenvalue λ 2 (p , Ω) of the anisotropic p -Laplacian − Q p u : = − div (F p − 1 (∇ u) F ξ (∇ u)) , where F is a suitable smooth norm of R n and p ∈ ] 1 , + ∞ [. We provide a lower bound of λ 2 (p , Ω) among bounded open sets of given measure, showing the validity of a Hong-Krahn-Szego type inequality. Furthermore, we investigate the limit problem as p → + ∞. [ABSTRACT FROM AUTHOR]

Abstract In this paper, several two-grid finite element algorithms for solving parabolic integro-differential equations (PIDEs) with nonlinear memory are presented. Analysis of these algorithms is given assuming a fully implicit time discretization. It is shown that these algorithms are as stable as the standard fully discrete finite element algorithm, and can achieve the same accuracy as the standard algorithm if the coarse grid size H and the fine grid size h satisfy H = O (h r − 1 r ). Especially for PIDEs with nonlinear memory defined by a lower order nonlinear operator, our two-grid algorithm can save significant storage and computing time. Numerical experiments are given to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to investigate some subordination implications for a class of nonlinear integral operators associated with multivalent functions in the open unit disk. Some known results associated with a class of nonlinear averaging integral operators are also pointed out as special cases of the main findings which are presented here. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and uniqueness of W 2 , p (n < p < ∞) solutions of a double obstacle problem. Moreover, we show the optimal regularity of the solution and the local C 1 regularity of the free boundary under a thickness assumption at the free boundary point on the intersection of two free boundaries. In the study of the regularity of the free boundary, we deal with a general problem, the no-sign reduced double obstacle problem with an upper obstacle ψ , F (D 2 u , x) = f χ Ω (u) ∩ { u < ψ } + F (D 2 ψ , x) χ Ω (u) ∩ { u = ψ } , u ≤ ψ in B 1 , where Ω (u) = B 1 ∖ { u = 0 } ∩ { ∇ u = 0 } . [ABSTRACT FROM AUTHOR]

• We propose a 5G NR- multiband for Radio over Fiber link outfitted with an optimized magnitude selective affine (OMSA) method to cover enhanced mobile broadband (eMBB) situations for 2.14 GHz and 10 GHz, correspondingly. • We show experimentally that OMSA further reduces the complexity with better or at least similar performance to that of MSA by using a weighted function as a nonlinear operator to accurately capture the nonlinear behaviour of the system being modelled, which can lead to a reduction in the number of segments and improvement in the accuracy of the model. This means that it will also lead to a reduction in the number of coefficients needed. This helps to make the model more efficient and simpler to use. • The experimental results demonstrate that the OMSA model has lower complexity than the MSA model while achieving a slightly better performance that is assessed in terms of computations, error vector magnitude (EVM) or adjacent channel power ratio (ACPR). The application of analog radio over fiber (A-RoF) systems for 5G new radio (NR) multiband waveforms presents challenges, including nonlinearity introduced by the Mach Zehnder Modulator and the dispersion and attenuation of the optical signal over long fiber lengths. To address these challenges, this paper proposes a new version of the magnitude-selective affine (MSA) model, named the optimized magnitude-selective affine (OMSA) model, which incorporates a power-reliant weighting function to improve performance while reducing complexity via Digital Predistortion (DPD). The OMSA model is tested using 5G NR signals at 10 GHz with 50 MHz and flexible-waveform signals at 2.14 GHz with a 20 MHz bandwidth, transmitted over a 10 km fiber length using a Mach Zehnder Modulator and a 1550 nm optical carrier. The performance of the OMSA model is compared to the MSA and generalized memory polynomial (GMP) models in terms of adjacent channel power ratio, error vector magnitude, and complexity. The results show that the OMSA model outperforms the MSA and GMP models in terms of performance reducing the error vector magnitude to 1.9% as compared to 4% and 3% in case of GMP and MSA respectively. Additionally, in terms of complexity measured via coefficients, OMSA is 168 times more efficient as compared to GMP and offers 1.93 times higher efficiency as compared to MSA while maintaining lower complexity. The experimental demonstration of 5G NR multiband waveforms over A-RoF links using the OMSA model represents a significant step towards the practical implementation of high-performance, low-complexity 5G NR systems over fiber-optic links and provides a promising solution to the challenges associated with DPD linearization for A-RoF systems. [ABSTRACT FROM AUTHOR]

Teaching Learning Algorithm (TLA) is a recently developed nature-inspired optimization technique applicable to complex optimization problems. This paper proposes an improved TLA version using the Laplacian operator of the Genetic Algorithm (GA), named LX-TLA. The proposed algorithm is tested on benchmark optimization problems, including unimodal and multimodal problems. The numerical results are obtained in the form of objective function values, and a t-test is applied to compare the performance of LX-TLA and basic TLA. Convergence plots are given to provide insight into the convergence behavior of LX-TLA. The results reveal that proposed algorithm provides effective and efficient performance in solving benchmark test functions. The proposed algorithm is also applied to engineering design problems, such as Tuned Mass Damper (TMD), truss structure, welded beam, tension string, and pressure vessel. The results obtained using LX-TLA are compared with other nature-inspired optimization algorithms. The results demonstrate that the proposed algorithm is a robust and effective tool for solving complex optimization problems. • Proposed an improved Teaching Learning Algorithm using Laplacian Operator of Genetic algorithm. • Tested on benchmarks functions of varying complexity. • Applied to real life problems in civil and mechanical engineering problems. [ABSTRACT FROM AUTHOR]

We use a bifurcation approach to investigate the dynamics of a planar switched system that alternates between two smooth systems of ODEs denoted as (L) and (R), respectively. For an x ∊ R that plays a role of bifurcation parameter, a switch to (R) occurs when the trajectory hits the switching line {x}xR and a switch to (L) occurs when the trajectory hits the switching line {-x}xR. This type of switching is known as relay, hysteresis, or hybrid switching in control. The main result of the paper gives suffcient conditions for bifurcation of an attracting or repelling limit cycle from a point O ∊ {0} xRR when x crosses 0. The result is achieved by identifying a region where the dynamics of the system is described by the map Px(y) = y + y2 +fβx/=y +o(y2): The map Px is obtained as a local return map induced by the switching line {x}x R. The fixed points of Px correspond to small amplitude limit cycles surrounding O. Motivated by applications to antilock braking systems, we focus on a particular class of switched systems where, for x=0, the point O is a so-called fold-fold singularity, i.e., the vector fields of both systems (L) and (R) are parallel to {0}xR at O. The result of the paper can be used for the design of switched control strategies that ensure limit cycling around a given point of the phase space. In particular, we illustrate the main theorem by establishing limit cycling behavior in relay affine systems (that model, e.g., power converters). Furthermore, we design a two-rule switched control to guarantee the existence of such an attracting limit cycle in antilock braking systems, whose magnitude can be made as small as necessary. This diminishes the need of additional switching rules used in other papers to not exceed the actuator technical capabilities. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of qualitative properties of flux-saturated type operators in dimension one. Specifically, we study regularity properties and smoothing effects, discontinuous interfaces, the existence of travelling wave profiles, sub- and supersolutions and waiting time features. The aim of the paper is to better understand these phenomena through two prototypic operators: the relativistic heat equation and the porous media flux-limited equation. As an important consequence of our results we deduce that solutions to the one-dimensional relativistic heat equation become smooth inside their support in the long time run. [ABSTRACT FROM AUTHOR]

We establish theorems on the existence and compactness of solutions to the σ 2 -Nirenberg problem on the standard sphere S 2. A first significant ingredient, a Liouville type theorem for the associated fully nonlinear Möbius invariant elliptic equations, was established in an earlier paper of ours. Our proof of the existence and compactness results requires a number of additional crucial ingredients which we prove in this paper: A Liouville type theorem for the associated fully nonlinear Möbius invariant degenerate elliptic equations, a priori estimates of first and second order derivatives of solutions to the σ 2 -Nirenberg problem, and a Bôcher type theorem for the associated fully nonlinear Möbius invariant elliptic equations. Given these results, we are able to complete a fine analysis of a sequence of blow-up solutions to the σ 2 -Nirenberg problem. In particular, we prove that there can be at most one blow-up point for such a blow-up sequence of solutions. This, together with a Kazdan-Warner type identity, allows us to prove L ∞ a priori estimates for solutions of the σ 2 -Nirenberg problem under some simple generic hypothesis. The higher derivative estimates then follow from classical estimates of Nirenberg and Schauder. In turn, the existence of solutions to the σ 2 -Nirenberg problem is obtained by an application of the by now standard degree theory for second order fully nonlinear elliptic operators. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new extragradient method with regularization for finding a common element of the solution set Γ of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in infinitedimensional Hilbert spaces, combining the regularization method and the technique of averaged operator, we prove the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)∩Γ under mild conditions. [ABSTRACT FROM AUTHOR]