Multiple positive solutions of a discrete difference system

摘要

This paper is concerned with the following systemΔ2u1(k)+f1(k,u1(k),u2(k))=0,k∈[0,T],Δ2u2(k)+f2(k,u1(k),u2(k))=0,k∈[0,T],u1(0)=u1(T+2)=0=u2(0)=u2(T+2).By using Leggett–Williams fixed point theorem, sufficient conditions are obtained for the existence of three positive solutions to the above system.