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

摘要

In this paper we consider the following boundary value problem of discrete systemΔ2u1(k)+f1(k,u1(k),u2(k))=0,k∈[0,T],Δ2u2(k)+f2(k,u1(k),u2(k))=0,k∈[0,T],with the Dirichlet boundary value conditionu1(0)=u1(T+2)=0=u2(0)=u2(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.