中文摘要：

非线性差分方程已经广泛应用于研究计算机科学、经济学、神经网络、生态学及控制论等学科中出现的离散模型。研究非线性差分方程边值问题解的存在性的方法主要有上下解方法,不动点定理,拓扑度理论等。值得注意的是,近几年来已有许多作者用临界点理论研究非线性差分方程边值问题解的存在性,这是很有力的工具。利用临界点理论研究一类二阶非线性差分方程边值问题多重解的存在性,提出一个新的判别方法。

英文摘要：

Nonlinear difference equations have been widely studied in many fields such as computer science,economics,neural network,ecology,cybernetics,etc.Nonlinear difference boundary value problems have been studied by many various methods,such as the upper and lower solution method,fixed point theorems,and topological degree theory.Also,in recent years,the critical point theory has played an important role in dealing with the existence and multiple results for nonlinear difference boundary value problems.By using critical point theory,the existence of multiple solutions for a class of second-order nonlinear difference boundary value problems is studied and a new sufficient condition is obtained