Existence uniqueness for a class of Nonlinear Discrete Boundary Value Problems

A monotone iterative method is proposed to solve nonlinear discrete boundary value problems with the support of upper and lower solutions. We establish some new existence results. Under some sufficient conditions, we establish maximum principle for linear discrete boundary value problem, which relies on Green’s function and its constant sign. We then use it to establish existence of unique solution for the nonlinear discrete boundary value problem ${\mathrm{\Delta }}^{2}y(t-1)=f(t,y(t)),t\in [1,T]$, $y(0)=0,y(T+1)=0$.