The Existence And Multiplicity Of The Solutions For The Boundary Value Problems Of 2mth-order Difference Equations

A class of boundary value problems for 2mth-order nonlinear difference equations are considered in this paper. By establishing the corresponding variational framework, the solutions of the boundary value problems are transformed into the critical points of the corresponding nonlinear functional. Then the existence of the critical points of the variational functional can be obtained by using the Linking Theorem and Saddle Point Theorem. That is to say, the existence of the solutions of the boundary value problems is obtained. Finally, some examples are given to illustrate the conclusion of this paper.This paper includes three chapters:In the first chapter, we introduce the background, significance and the latest development of the problems which we discuss. In order to facilitate the discussion behind, we introduce the relevant preparation knowledge. And we also describe the main work of this paper.In chapter 2, by using the Saddle Point Theorem, we discuss the boundary value problems for 2mth-order nonlinear difference equations, and obtain the conditions of the existence of the solutions.In chapter 3, by using the Linking Theorem, we discuss the boundary value problems for 2mth-order nonlinear difference equations, and obtain the conditions of the multiplicity of the solutions.