Existence of a priori bounded solutions for discrete two-point boundary value problems

In this paper, a careful analysis on the existence of a priori bounded solutions for difference equations is provided. In particular, we study a second order nonlinear difference boundary value problem and its relationship with the continuous one and we obtain a version of these existence results with a priori bounds of the solution u and its derivative u′,u″ and we give an analytic expression of the solution u as the limit of a suitable sequence of functions.