Existence of positive solutions of BVPs for third-order discrete nonlinear difference systems

In this paper we consider the following boundary value problem of discrete system (Delta(3) u(1)(k) + f(1)(k,u(1)(k), u(2)(k)) = 0, kis an element of[0,T] (Delta(3) u(2)(k) + f(2)(k,u(1)(k), u(2)(k)) = 0, kis an element of[0,T] with the Dirichlet boundary condition u(1)(0) = u(1)(1) = u(1)(T + 3) = 0 = u(2)(0) = u(2)(1) = u(2)(T + 3). Some 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. (C) 2003 Elsevier Inc. All rights reserved.