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Abstract: In this paper, we consider the following p-Laplacian multipoint boundary value problem on time scales:where , , , . By using fixed point index, we provide some sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. Especially, the nonlinear term is allowed to change sign. As an application, an example is given to demonstrate our 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: Necessary and sufficient conditions are obtained for the existence of symmetric positive solutions to the boundary value problem Applications of our results to the special case where f is a power function of u and its derivatives are also discussed. Moreover, similar conclusions for a more general higher order boundary value problem are established. Our results extend some recent work in the literature on boundary value problems for ordinary differential equations. The analysis of this paper mainly relies on fixed point theorems on cones. [Copyright &y& Elsevier]

Abstract: In this paper, the three-point boundary value problem and its conjugate boundary value problem are studied under some conditions concerning the same first eigenvalue of the both linear problems. By applying the fixed point index theory, the coexistence of single and multiple positive solutions of the above mentioned problems is verified. As an application, some examples are given to illustrate our results. [Copyright &y& Elsevier]

Abstract: In this paper, the second-order four-point boundary value problem is studied, where , , and , are nonnegative continuous functions. By the use of the property of the corresponding Green''s function, fixed-point index theory, Leray–Schauder degree and upper and lower solution method, some existence, nonexistence, and multiplicity results of positive solutions are acquired. [Copyright &y& Elsevier]

Abstract: In this paper we consider the existence of positive solutions of the following boundary value problem: where are the increasing homeomorphism and positive homomorphism and , . We show the sufficient conditions for the existence of positive solutions by using the nome type cone expansion–expression fixed point theorem. [Copyright &y& Elsevier]

Abstract: In this paper, by using the cone theory and the monotone iterative technique, we investigate the existence of maximal and minimal solutions of the initial value problem for second order impulsive differential equations which nonlinearly involve the derivative in Banach space and give an example to illustrate our results. [Copyright &y& Elsevier]

Abstract: In this paper we study the existence of positive solutions of the equation where is an increasing homeomorphism and homomorphism and , subject to linear mixed boundary conditions by a simple application of a fixed point index theorem in cones. [Copyright &y& Elsevier]

Abstract: In this paper the existence and nonexistence results of positive solutions are obtained for Sturm–Liouville boundary value problem where , , , for , , are constants and satisfy . The discussion is based on the positivity estimation for the Green''s function of associated linear boundary value problem and the fixed point index theory in cones. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate an m-point boundary value problem with sign changing nonlinearity. The existence of an interval of parameters which ensures the problem has at least one positive solution is determined by constructing available operator and combining the method of lower solution with the method of topology degree. Moreover, the associated Green''s function for the above problem is also given. [Copyright &y& Elsevier]

Abstract: By using fixed point theorem of cone expansion and compression, this paper investigates the existence of multiple positive solutions for singular boundary value problems of a coupled system of nonlinear ordinary differential equations. [Copyright &y& Elsevier]

In this paper, by means of a new twin fixed-point theorem in a cone, the existence of at least two positive solutions of m-point boundary value problem for second order dynamic equations on time scales is considered. [Copyright &y& Elsevier]

In this paper the existence results of positive solutions are obtained for fourth-order boundary value problem u(4)+βu″−αu=f(t,u), 0f :[0,1]×R+→R+ is continuous, α,β∈R and satisfy β<2π2, α&ges;−β2/4, α/π4+β/π2<1. [Copyright &y& Elsevier]