Existence of positive solution for second-order nonlinear discrete system with parameter

This paper is concerned with the following discrete system,Δ2ui(k)+λhi(k)fi(u1(k),u2(k),…,un(k))=0,k∈[0,T],i=1,2…,n,ui(0)=ui(T+2)=0,i=1,2,⋯,n.By using the theory of the fixed-point index, sufficient conditions are obtained for the existence of positive solution to the above system.