Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem

This paper is concerned with the existence of solutions for the discrete second-order boundary value problem Δ2u(t-1)+λ1u(t)+g(Δu(t))=f(t), t∈{1,2,…,T}, u(0)=u(T+1)=0, where T>1 is an integer, f:{1,…,T}→R, g:R→R is bounded and continuous, and λ1 is the first eigenvalue of the eigenvalue problem Δ2u(t-1)+λu(t)=0, t∈T, u(0)=u(T+1)=0