Difference Equation Solution Of The Existence Of The Critical Point

In this paper, the critical point theory is employed to investigate the existence and multiple solutions for some difference boundary value problems.In the first chapter, by means of lemmas on coercive map and even functional, we established theorems for the existence of at least n-1 distinct pairs solutions for a second-order difference periodic boundary value problem.In the second chapter, by using mountain lemma, existence of solutions for a fourth-order difference boundary value problem is studied. Several examples are given to illustrate the application of our results.