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In this paper, we consider a class of nonlinear third-order boundary value problems with integral boundary conditions on time scales. By applying a generalization of the Leggett-Williams fixed point theorem, we establish the existence of at least three positive solutions. The discussed problem involves both an increasing and positive homomorphism, which generalizes the p-Laplacian operator. As an application, we give an example to illustrate our results. [ABSTRACT FROM AUTHOR]

We investigate the sharp L p → L r {L^{p}\to L^{r}} estimates for the restricted averaging operator A C {A_{C}} over the cone C of the d-dimensional vector space 𝔽 q d {\mathbb{F}_{q}^{d}} over the finite field 𝔽 q {\mathbb{F}_{q}} with q elements. The restricted averaging operator A C {A_{C}} for the cone C is defined by the relation A C ⁢ f = f ∗ σ | C {A_{C}f=f\ast\sigma|_{C}} , where σ denotes the normalized surface measure on the cone C, and f is a complex-valued function on the space 𝔽 q d {\mathbb{F}_{q}^{d}} with the normalized counting measure dx. In the previous work [D. Koh, C.-Y. Shen and I. Shparlinski, Averaging operators over homogeneous varieties over finite fields, J. Geom. Anal. 26 2016, 2, 1415–1441], the sharp boundedness of A C {A_{C}} was obtained in odd dimensions d ≥ 3 {d\geq 3} , but only partial results were given in even dimensions d ≥ 4 {d\geq 4}. In this paper we prove the optimal estimates in even dimensions d ≥ 6 {d\geq 6} in the case when the cone C ⊂ 𝔽 q d {C\subset\mathbb{F}_{q}^{d}} contains a d / 2 {{d/2}} -dimensional subspace. [ABSTRACT FROM AUTHOR]

In this paper, we will use the Krasnosel'skii fixed point theorem to investigate a discrete fractional boundary value problem of the form -Δvy(t) = λh(t+v-1)f(y(t+v-1)),y(v-2) =Ψ(y),y(v+b) =Φ(y), where 1N0,f: [0,∞)→[0,∞) is a continuous function, h: [v-1, v+b-1]Nv-1→[0,∞), Ψ,Φ: Rb+3→R are given functionals, where Ψ,Φ are linear functionals, and λ is a positive parameter. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study the existence, localization and multiplicity of positive solutions for a (2m)th-order boundary value problem subject to the Dirichlet conditions. Our approach is based on critical point theory in conical shells and Harnack type inequalities. [ABSTRACT FROM AUTHOR]

A reverse experiment technique is used along with the technology of measuring rods to study the impact and penetration of a steel conical body in frozen sandy soil. This paper presents the dependences of maximum values of the force of resistance of cones with base diameters of 10.0, 12.0, and 19.8 mm to penetration into sand on the impact velocity in the range of values 100-400 m/s. The numerical solution of the problem in an axisymmetric formulation with the use of the “Dinamika-2” software package is used to show the effect of waves reflected from the walls of the container on the contact force. A comparative analysis of the forces of resistance to penetration of the shocker into compacted dry, water-saturated, and frozen sandy soils is carried out. [ABSTRACT FROM AUTHOR]

On complete Riemannian manifolds, a geodesic linking two different points could be approximated by applying short ruler methods to shorten a given path iteratively. In this paper we take a closer look at a short ruler method on a cone. To handle the problems caused by the fact that the cone is not smooth at its apex, we unwind the cone isometrically into the plane, and show that the sequence of shortened curves converges to a geodesic. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point results for contractive type conditions in the framework of complete cone b-metric spaces and give some applications of our results. The results presented in this paper generalize, extend and unify several well-known comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we compute the Möbius function of pointed integer partition and pointed ordered set partition using topological and analytic methods. We show that the associated order complex is a wedge of spheres and compute the associated reduced homology group for each subposet. In addition, we compute the Möbius function of pointed graded lattice and use our method to compute the Möbius function of pointed direct sum decomposition of vector spaces. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of positive radial solutions of the elliptic equation with nonlinear gradient term where,,is continuous. Under the conditions that the nonlinearitymay be of superlinear or sublinear growth inuand, existence results of positive radial solutions are obtained. For the superlinear case, the growth offinis restricted to quadratic growth. The superlinear and the sublinear growth of the nonlinearity offare described by inequality conditions instead of the usual upper and lower limits conditions. Our discussion is based on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to obtain a general theorem on existence of continuous branch of solutions of equations which depend on a parameter by using the monotone minorant method in conjunction with the theory of fixed point index. As an application, we apply this theorem to prove the existence of a positive eigen-pair of multivalued homogeneous increasing operators. The simplicity and uniqueness of the eigen-pair are also investigated in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions to the boundary-value problem with fractional order (CaDαy)(t) +q(t)f(y) = 0, 0 ≤ a < t < b, 1 < α < 2, y(a) = 0, y(b) = βy(η), where a < η < b and β(η − a) − b + a ≠ 0. We prove the existence of at least one positive solution when f is either superlinear or sublinear using the well-known Guo-Lakshmikantham fixed point theorem in cones. Moreover, the convexity and concavity of the solutions are investigated with respect to the behavior of the function q. [ABSTRACT FROM AUTHOR]

In this paper we investigate a parameter-dependent nonlocal differential equations with convolution coefficients. Using the Birkhoff–Kellogg type theorem, existence of positive solutions is established. Under additional growth conditions, we obtain upper and lower bounds for the parameter. An example is also given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, as the extension of the isotonicity of the metric projection, the isotonicity characterizations with respect to two arbitrary order relations induced by cones of the metric projection operator are studied in Hilbert spaces, when one cone is a subdual cone and some relations between the two orders hold. Moreover, if the metric projection is not isotone in the whole space, we prove that the metric projection is isotone in some domains in both Hilbert lattices and Hilbert quasi-lattices. By using the isotonicity characterizations with respect to two arbitrary order relations of the metric projection, some solvability and approximation theorems for the complementarity problems are obtained. Our results generalize and improve various recent results in the field of study. [ABSTRACT FROM AUTHOR]

This paper considers a class of fractional impulsive wave equations and improves a previous results. In fact, this paper adopts a new topological approach to prove the existence of classical solutions with a complex arguments caused by impulsive perturbations. To the best of our knowledge, there is a severe lack of results related to such impulsive equations.

This paper discusses the natural convection boundary layer flow of a micropolar nanofluid over a vertical permeable cone with variable wall temperatures. Non-similar solutions are obtained. The nonlinearly coupled differential equations under the boundary layer approximations governing the flow are solved numerically using an efficient, iterative, tri-diagonal, implicit finite difference method. Different experimental correlations for both nanofluid effective viscosity and nanofluid thermal conductivity are considered. It is found that as the vortex-viscosity parameter increases, both the velocity profiles and the local Nusselt number decrease. Also, among all the nanoparticles considered in this investigation, Cu gives a good convection. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of positive solutions for the iterative system of nonlinear dynamic equations on time scales ... satisfying the m-point boundary conditions ... by applying Guo-Krasnosel'skii fixed point theorem. [ABSTRACT FROM AUTHOR]

In this article, we study the existence and the uniqueness of iterative positive solutions for a class of nonlinear singular integral equations in which the nonlinear terms may be singular in both time and space variables. By using the fixed point theorem of mixed monotone operators in cones, we establish the conditions for the existence and uniqueness of positive solutions to the problem. Moreover, we derive various properties of the positive solutions to the equation and establish their dependence on the model parameter. The theorem obtained in this paper is more general and complements many previous known results including singular and nonlinear cases. Application of the results to the study of differential equations are also given in the article. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and multiplicity of positive solutions for a class of systems of fractional differential equation with parameters. By applying the Krasnosel'skii fixed point theorem for a cone map, we conclude to the existence of at least one and two solutions for our considered system. [ABSTRACT FROM AUTHOR]

In this paper, we give improved results on the existence of positive solutions for the following one-dimensional p-Laplacian equation with nonlinear boundary conditions: where $\phi_{p} ( s ) = | s | ^{ p-2 } s$ , $p >1 $ . Constructing an available integral operator and combining fixed point index theory, we establish some optimal criteria for the existence of bounded positive solutions. The interesting point of the results is that the term $b ( t ) $ may be singular at $t=0$ and/or $t=1$ . Moreover, the nonlinear term $g(t, y)$ is also allowed to have singularity at $y=0$ . In particular, our results extend and unify some known results. [ABSTRACT FROM AUTHOR]

In this paper, by constructing a cone K × K in the Cartesian product space C[0, 1] × C[0, 1], and using spectral analysis of the relevant linear operator for the corresponding differential system, some properties of the first eigenvalue corresponding to the relevant linear operator are obtained, and the fixed-point index of nonlinear operator in the K × K is calculated explicitly and the existence of at least one positive solution or two positive solutions of the singular differential system with integral boundary conditions is established. [ABSTRACT FROM AUTHOR]

In this paper, we study the distributional Henstock-Kurzweil integral and its properties, such as strong and weak convergence theorems. We also establish the structure of the space of Henstock-Kurzweil integrable distributions, which is proved to be an ordered Banach space with a regular cone. Furthermore, fixed point theorems in such space are presented to deal with nonlinear integral equations involving this integral. [ABSTRACT FROM AUTHOR]

In this paper, by Leggett-William fixed point theorem, we establish the existence of triple positive solutions of a new kind of integral boundary value problem for the nonlinear singular differential equations with p-Laplacian operator, in which q(t) can be singular at t = 0; 1. We also show that the results obtained can be applied to study certain higher order mixed boundary value problems. At last, we give an example to demonstrate the use of the main result of this paper. The conclusions in this paper essentially extend and improve the known results. [ABSTRACT FROM AUTHOR]

This paper weals with the existence of positive solutions of the fully second-order boundary value problem [ABSTRACT FROM AUTHOR]

In this paper, we consider nonlinear second order m-point impul- sive time scale boundary value problems on infinite intervals. We establish criteria for the existence of positive solutions to the nonlinear impulsive time scale boundary value problems on infinite intervals by using a result from the theory of fixed point index. [ABSTRACT FROM AUTHOR]

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In this paper, we consider the higher-order multi-point fractional boundary value problem. We establish the criteria for the existence of at least one and three positive solutions for higher order nonlinear m-point fractional boundary value problem by using the Krasnosel'skii fixed point theorem and the Legget-Williams fixed point theorem, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we consider a higher order p-Laplacian differential equations, By applying Five functional fixed point theorem, we establish sufficient conditions for the existence of triple positive solutions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a set-valued solution of the following Pexider functional equation F(ax + by) = ΑG(x) + βH(y) with three unknown functions F, G and H, where a, b, Α β are positive real scalars. [ABSTRACT FROM AUTHOR]

In this paper, by using the Guo-Krasnoselskii theorem, we investigate the existence and nonexistence of positive solutions of a system of integral equation with parameters which can be seen as an effective generalization of various types of systems of boundary value problems for differential equation on continuous interval and time scales or fractional differential equations. We give a general approach of positive solutions to cover various systems of boundary value problems in a unified way, which avoids treating these problems on a case-by-case basis. Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution, respectively. By giving some examples, we will show how our results may be applied to consider existence of positive solutions to a variety of system of boundary value problems of differential equations, differential equations on time scales or fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, by using Leray-Schauder fixed-point theorem, Avery-Henderson fixed-point theorem and Leggett-Williams fixed-point theorem, respectively, we investigate the conditions for the existence of at least one, two and three positive solutions to nonlinear second-order impulsive boundary value problems on time scales. [ABSTRACT FROM AUTHOR]

This paper deals with the existence and multiplicity of positive solutions for a system of nonlinear singular higher-order fractional differential equations with fractional multi-point boundary conditions. The main tool used in the proof is fixed point index theory. Some limit type conditions for ensuring the existence of positive solutions are given, and our conditions are suitable for more general functions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to discuss boundary value problems of fractional differential equations with $p(t)$-Laplacian operator. Some new existence, uniqueness, and multiplicity results were acquired by employing some fixed point theorems. Moreover, some examples are supplied to verify our main results. [ABSTRACT FROM AUTHOR]

Let E be a real normed linear space. A subset X ⊂ E is called a retract of E if there exists a continuous mapping r : E → X, a retraction, satisfying r(x) = x, x ⊂ X. It is well known that every nonempty closed convex subset of E is a retract of E. Nonconvex retracts are studied in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the stability of a class of nonautonomous nonlinear difference equations that are determined by functions which satisfy certain contractive type condition is studied in metric spaces, and its variant problem in ordered Banach spaces is also investigated. Several examples are given to illustrate their applications. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence, nonexistence, uniqueness, and multiplicity of positive solutions for a class of eigenvalue problems of nonlinear fractional differential equations with a nonlinear integral term and a disturbance parameter in the boundary conditions. By using fixed point index theory we give the critical curve of eigenvalue λ and disturbance parameter μ that divides the range of λ and μ for the existence of at least two, one, and no positive solutions for the eigenvalue problem. Furthermore, by using fixed point theorem for a sum operator with a parameter we establish the maximum eigenvalue interval for the existence of the unique positive solution for the eigenvalue problem and show that such a positive solution depends continuously on the parameter λ for given μ. In particular, we give estimates for the critical value of parameters. Two examples are given to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear higher order three-point boundary value problem on time scales. We establish the criteria for the existence of one or two positive solutions for a higher order boundary value problem on time scales by using a result from the theory of fixed point index. Later, Leggett-Williams fixed-point theorem is used to investigate the existence of at least three positive solutions for a higher order boundary value problem on time scales. As an application, to demonstrate our results we also give an example. [ABSTRACT FROM AUTHOR]

In this paper, we construct a modified Green's function with respect to the stationary Schrödinger operator on cones. As applications, we not only obtain the boundary behaviors of generalized harmonic functions but also characterize the geometrical properties of the exceptional sets with respect to the Schrödinger operator. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of fixed points for nonlinear and semilinear operators on order intervals. The abstract results unified some methods in studying the existence of positive solutions for boundary and initial value problems of nonlinear difference and differential equations. Applications are shown by examples. [ABSTRACT FROM AUTHOR]

Suppose that M is a strictly convex and closed hypersurface in En+1 with the origin o in its interior. We consider the homogeneous function g of positive degree d satisfying M = g −1(1) . Then, for a positive number h the level hypersurface g −1(h) of g is a homothetic hypersurface of M with respect to the origin o. In this paper, for tangent hyperplanes Φh to g −1(h) (0 < h < 1), we study the (n + 1) -dimensional volume of the region enclosed by Φh and the hypersurface M, etc.. As a result, with the aid of the theorem of Blaschke and Deicke for proper affine hypersphere centered at the origin, we establish some characterizations for ellipsoids in En+1 . As a corollary, we extend Schneider’s characterization for ellipsoids in E3 . Finally, for further study, we raise a question for elliptic paraboloids which was originally conjectured by Golomb. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and multiplicity of positive solutions for a nonlinear fourth-order ODE with multi-point boundary conditions and an integral boundary condition. The main tool is Krasnosel'skii fixed point theorem on cones. [ABSTRACT FROM AUTHOR]

The modern genus Dacrycarpus (Endl.) de Laub. of the family Podocarpaceae, containing nine species, is mainly distributed in tropical mountain rainforests of the southwestern Pacific region, ranging from New Zealand to low‐latitude Asia. This genus has abundant fossil records in both hemispheres, but all the known megafossils were limited to Australasia and South America. Here we report on Dacrycarpus guipingensis sp. nov. from the Miocene Erzitang Formation of Guangxi, South China. This is the first megafossil of Dacrycarpus in the Northern Hemisphere. The new species is represented by mummified dimorphic foliage, ovuliferous shoots, and a male cone with in situ pollen. It resembles the extant Dacrycarpus imbricatus (Blume) de Laub., which is common in rainforests from southern China and northern Myanmar to Fiji. This paper presents the first data on the anatomical structure of seed cone and exine ultrastructure of Dacrycarpus in situ pollen grains from a fossil material by using computed tomography scanning and ultrathin sectioning. For comparative purpose, data on the pollen morphology and ultrastructure were obtained for modern D. imbricatus for the first time. The D. guipingensis fossils strongly suggest the Miocene arrival of Dacrycarpus in Asia from the Southern Hemisphere. Based on the modern ecological niche and related fossil elements, this fossil locality was probably covered by conifer–broad‐leaved mountain rainforests during the Miocene. [ABSTRACT FROM AUTHOR]