Existence of positive solutions of boundary value problem for a discrete difference system

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