Existence of positive solutions of BVPs for second-order nonlinear difference systems

摘要

This paper is concerned with the following systemDelta(2)u(i)(k) + f(i)(k, u(1)(k), u(2)(k),..., u(n)(k)) = 0, k is an element of [0, T], i = 1, 2,..., nwith the Dirichlet boundary conditionu(i)(0) = u(i)(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. (C) 2003 Elsevier Inc. All rights reserved.