Multiple positive solutions of BVPs for third-order discrete difference systems

摘要

This paper is concerned with the following 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).By using Leggett–Williams fixed point theorem, sufficient conditions are obtained for the existence of three positive solutions to the above system.