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

摘要

In this paper we consider the following boundary value problem of discrete systemΔ3u1(k)+f1(k,u1(k),u2(k))=0,k∈[0,T],Δ3u2(k)+f2(k,u1(k),u2(k))=0,k∈[0,T],with the Dirichlet boundary conditionu1(0)=u1(1)=u1(T+3)=0=u2(0)=u2(1)=u2(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.