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

摘要

This paper is concerned with the existence of solutions for the discrete second-order boundary value problemΔ2u(t-1)+λ1u(t)+g(Δu(t))=f(t),t∈{1,2,…,T},u(0)=u(T+1)=0, whereT>1is an integer,f:{1,…,T}→ℝ,g:ℝ→ℝis bounded and continuous, andλ1is the first eigenvalue of the eigenvalue problemΔ2u(t-1)+λu(t)=0,t∈𝕋,u(0)=u(T+1)=0.