Search

Abstract: In this paper we consider the following n-dimensional second-order nonlinear system on time scaleswith the Sturm–Liouville boundary conditionswhere , , . Let and . Define number of zeros in the set and number of infinities in the set By using fixed point index theory, we show that: [(i)] if or 2, then there exist such that the system has positive solution(s) for [(ii)] if or 2, then there exist such that the system has positive solution(s) for [(iii)] if or , then the system has no positive solution for sufficiently large or small , respectively. [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 consider the following nonlinear first-order periodic boundary value problems on time scales Some new existence and multiplicity criteria of positive solutions are established by using several well-known fixed point theorems. [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: 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]

This paper is concerned with the following systemΔ2ui(k)+fi(k,u1(k),u2(k),…,un(k))=0, k∈[0,T], i=1,2,…,nwith the Dirichlet boundary conditionui(0)=ui(T+2)=0, i=1,2,…,n.Some new results are obtained for the existence and multiplicity of positive solutions to the above system by using nonlinear alternative of Leray–Schauder type, Krasnosel''skii''s fixed point theorem in a cone and Leggett–Williams fixed point theorem. In particular, it proves that the above system has N positive solutions under suitable conditions, where N is an arbitrary integer. [Copyright &y& Elsevier]

This paper is concerned with the following systemΔ3u1(k)+f1(k,u1(k),u2(k))=0,k∈[0,T],Δ3u2(k)+f2(k,u1(k),u2(k))=0,k∈[0,T],with the Dirichlet boundary conditionu1(0)=u1(1)=u1(T+3)=0=u2(0)=u2(1)=u2(T+3).By using Leggett–Williams fixed point theorem, sufficient conditions are obtained for the existence of three positive solutions to the above system. [Copyright &y& Elsevier]

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

In this paper, we consider the following dynamical system on a measure chain: u1ΔΔ(t)+f1(t,u1(σ(t)),u2(σ(t)))=0, t∈[a,b],u2ΔΔ(t)+f2(t,u1(σ(t)),u2(σ(t)))=0, t∈[a,b],with the Sturm–Liouville boundary value conditionsαui(a)−βuiΔ(a)=0, γui(σ(b))+δuiΔ(σ(b))=0 for i=1,2.Some results are obtained for the existence of three positive solutions of the above problem by using Leggett–Williams fixed point theorem. [Copyright &y& Elsevier]

In this paper, existence criteria for three positive solutions of the nonlinear three-point boundary value problem u″(t)+a(t)u′(t)+b(t)u(t)+h(t)f(u)=0, t∈(0,1),u(0)=0, u(1)=αu(η), are established by using the Leggett–Williams fixed point theorem. An example is also included to illustrate the importance of the result obtained. [Copyright &y& Elsevier]

This paper is concerned with the following systemΔ2u1(k)+f1(k,u1(k),u2(k))=0, k∈[0,T],Δ2u2(k)+f2(k,u1(k),u2(k))=0, k∈[0,T],u1(0)=u1(T+2)=0=u2(0)=u2(T+2).By using Leggett–Williams fixed point theorem, sufficient conditions are obtained for the existence of three positive solutions to the above system. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the following discrete system,By using the theory of the fixed-point index, sufficient conditions are obtained for the existence of positive solution to the above system. [Copyright &y& Elsevier]