Search

Abstract: This paper is concerned with the existence of positive solutions of -Laplacian dynamic equation subject to boundary conditions or , where with . By using the five functionals fixed-point theorem, we prove that the boundary value problem has at least three positive solutions. As an application, an example is given to illustrate the result. [Copyright &y& Elsevier]

Abstract: Let be a time scale such that . By the Schauder fixed-point theorem and the upper and lower solution method, we present some existence criteria of the positive solution of m-point singular p-Laplacian dynamic equation with boundary conditions , where with , is continuous for and nonincreasing if . The nonlinear term may be singular in its dependent variable and is allowed to change sign. Our results are new even for the corresponding differential and difference equations . As an application, an example is given to illustrate our result. [Copyright &y& Elsevier]

Abstract: Let be a time scale such that . We consider the three-point boundary value problem for -Laplacian dynamic equations on time scales of the form for with boundary conditions , , where is symmetric in and with . By using a pseudo-symmetric technique and the five-functionals fixed-point theorem, we prove that the boundary value problem has at least three positive pseudo-symmetric solutions under some assumptions. As an application, an example is given to illustrate the result. [Copyright &y& Elsevier]

Abstract: In this paper we consider the one-dimensional p-Laplacian boundary value problem on time scales where is p-Laplacian operator, i.e., , . Some new results are obtained for the existence of at least single, twin or triple positive solutions of the above problem by using Krasnosel''skii''s fixed point theorem, new fixed point theorem due to Avery and Henderson and Leggett–Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian boundary value problems on time scales has been studied. [Copyright &y& Elsevier]

Abstract: In this paper we are concerned with the following nonlinear first-order periodic boundary value problem on time scales Some new existence criteria of at least one solution are established by using novel inequalities and the well-known Schaefer fixed point theorem. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence and multiplicity of the solutions for the fourth-order boundary value problem , , , where is continuous, and are parameters. Using the variational structure of the above boundary value problem and critical point theory, it is shown that the different locations of the pair and lead to different existence results for the above boundary value problem. More precisely, if the pair is on the left side of the first eigenvalue line, then the above boundary value problem has only the trivial solution for and has infinitely many solutions for ; if is on the right side of the first eigenvalue line and , then the above boundary value problem has two nontrivial solutions or has at least distinct pairs of solutions, which depends on the fact that the pair is located in the second or fourth (first) quadrant. [Copyright &y& Elsevier]

Abstract: In this paper, an existence criterion is established for a class of second order perturbed dynamic inclusions on time scales with boundary conditions. The main approach is a fixed-point theorem for multi-valued maps due to Dhage. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the controllability of a certain class of evolution differential inclusions in Banach spaces. A sufficient condition is established by using a recent fixed-point theorem for multi-valued maps due to Dhage combined with an evolution system. An example is also given to illustrate our result. [Copyright &y& Elsevier]

Abstract: In this paper we study the existence and multiplicity of the solutions for the fourth-order boundary value problem (BVP) , , , where is continuous, and are parameters. By means of the idea of the decomposition of operators shown by Chen [W.Y. Chen, A decomposition problem for operators, Xuebao of Dongbei Renmin University 1 (1957) 95–98], see also [M. Krasnosel''skii, Topological Methods in the Theory of Nonlinear Integral Equations, Gostehizdat, Moscow, 1956], and the critical point theory, we obtain that if the pair is on the curve satisfying , then the above BVP has at least one, two, three, and infinitely many solutions for λ being in different interval, respectively. [Copyright &y& Elsevier]

Abstract: Let be a time scale such that , a i ⩾0 for i =1,…, m −2. Let ξ i satisfy 0< ξ 1 < ξ 2 <⋯< ξ m−2 < ρ(T) and . We consider the following p-Laplacian m-point boundary value problem on time scaleswhere a ∈ C ld ((0, T),[0,∞)) and f ∈ C ld ((0, T)×[0,∞),[0,∞)). Some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems respectively. In particular, our criteria extend and improve some known results. [Copyright &y& Elsevier]

Abstract: In this paper we are concerned with the following system of nonlinear first-order periodic boundary value problems on time scale where is continuous and there exists a constant such thatSome existence criteria of positive solution are established by using a fixed point theorem for operators on cone. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence and nonexistence of positive solutions of the nonlinear fourth-order beam equation , , , where is continuous and ζ, η and λ are parameters. We show that there exists a such that the above boundary value problem (BVP) has at least two, one and no positive solutions for , and , respectively. Furthermore, by using the semiorder method on cones of Banach space, we establish a uniqueness criterion for positive solution of the BVP. In particular such a positive solution of the BVP depends continuously on the parameter λ, i.e., is nondecreasing in λ, and for any . [Copyright &y& Elsevier]

Abstract: Let be a time scale such that . Consider the following three-point boundary value problem on time scales: where , , , , and . By using fixed point theorems in cones, some new and general results are obtained for the existence of single and multiple positive solutions of the above problem. In particular, our criteria generalize and improve some known results. [Copyright &y& Elsevier]

In this paper we consider the following boundary value problem of discrete systemwith the Dirichlet boundary conditionSome new results of the existence, nonexistence and multiplicity are obtained by using Krasnosel''skii''s fixed point theorem in a cone. In particular, it is proved that the above boundary value problem has N positive solutions under suitable conditions, where N is an arbitrary positive integer. [Copyright &y& Elsevier]

In this paper we consider the following boundary value problem of discrete systemwith the Dirichlet boundary value conditionSome sufficient conditions are obtained for the existence of one or two positive solutions to the above system by using nonlinear alternative of Leray–Schauder type and Krasnosel''skii''s fixed point theorem in a cone. [Copyright &y& Elsevier]