Existence of positive solutions of BVPs for second-order nonlinear difference systems

摘要

This paper is concerned with the following systemΔ2ui(k)+fi(k,u1(k),u2(k),…,un(k))=0,k∈[0,T],i=1,2,…,nwith the Dirichlet boundary conditionui(0)=ui(T+2)=0,i=1,2,…,n.Some new results are obtained for the existence and multiplicity of positive solutions to the above system by using nonlinear alternative of Leray–Schauder type, Krasnosel'skii's fixed point theorem in a cone and Leggett–Williams fixed point theorem. In particular, it proves that the above system has N positive solutions under suitable conditions, where N is an arbitrary integer.