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In this paper, we study the blow-up profiles of the nonlocal dispersal equation. More precisely, we prove that the positive solution of nonlocal dispersal equation has different blow-up profiles, depending on the refuge domain. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the following nonlinear first-order periodic boundary value problem with parameter on a time scale where is a parameter. For suitable , some existence, multiplicity and nonexistence criteria of positive solutions are established by using well-known results from the fixed-point index. [Copyright &y& Elsevier]

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: We investigate a class of singular -point -Laplacian boundary value problem on time scales with the sign changing nonlinearity. By using the well-known Schauder fixed point theorem and upper and lower solutions method, some new existence criteria for positive solutions of the boundary value problem are presented. These results are new even for the corresponding differential and difference equations , as well as general time scales setting. As an application, an example is given to illustrate the results. [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: This paper is concerned with the following system on time scale : where and . By using the theory of the fixed point index, we investigate the effect of on the existence and nonexistence of positive solution for the above system in sublinear cases. The results obtained are even new for the special cases of difference system and differential system, as well as in the general time scale setting. [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]

Let $${\Bbb T}$$ be a time scale such that 0, T ∈ $${\Bbb T}$$ . By means of the Schauder fixed point theorem and analysis method, we establish some existence criteria for positive solutions of the m–point boundary value problem on time scales where a ∈ C ld ((0, T), [0,∞)), f ∈ C ld ([0,∞) × [0,∞), [0,∞)), β, γ ∈ [0,∞), ξ i ∈ (0, ρ( T)), b, a i ∈ (0,∞) (for i = 1, . . . , m− 2) are given constants satisfying some suitable hypotheses. We show that this problem has at least one positive solution for sufficiently small b > 0 and no solution for sufficiently large b. Our results are new even for the corresponding differential equation ( $${\Bbb T}$$ = ℝ) and difference equation ( $${\Bbb T}$$ = ℤ). [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the existence and nonexistence of positive solutions of the second-order nonlinear dynamic equation , , satisfying either the conjugate boundary conditions or the right focal boundary conditions , where a and f are positive. We show that there exists a such that the above boundary value problem has at least two, one and no positive solutions for , and , respectively. Furthermore, by using the semiorder method on cones of the Banach space, we establish an existence and uniqueness criterion for positive solution of the problem. In particular, such a positive solution of the problem depends continuously on the parameter λ, i.e., is nondecreasing in λ, and . [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]

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, the existence of multiple positive solutions to the second-order Neumann BVPs−u′′+Mu=f(t,u), u′(0)=u′(1)=0andu′′+Mu=f(t,u), u′(0)=u′(1)=0are proved by a fixed point theorem in cone due to Krasnoselskii. [Copyright &y& Elsevier]

This paper studies the existence, global stability and uniform persistence of positive periodic solutions of a periodic predator–prey system with Holling type III functional response. By using the continuation theorem of coincidence degree theory and Liapunov functional, some sufficient conditions are obtained. [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]

Classification schemes for positive solutions of a class of higher-order nonlinear delay difference equations are given in terms of their asymptotic behavior, and necessary as well as sufficient conditions for the existence of these solutions are also provided. [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]