On The Existence Of Solutions For A Fourth-Order Discrete Boundary Value Problem

This paper mainly concerns with the existence and multiplicity of solutions for a class of non-linear fourth-order discrete boundary value problems by using the crit-ical point theory. We reduces the problem of finding solutions of a boundary value problem to that of seeking critical points of the corresponding functional on a suitable function space. We establish various sets of sufficient conditions on the nonexistence and existence of solutions for the boundary value problems of difference equations. This dissertation is composed of four chapters.Chapter 1 concentrates on the brief introduction of historic background and significance for the investigated problems, preliminaries, existence results and main works.In Chapter 2, we establish the corresponding variational functional and devote to the study of the nonexistence of nontrivial solutions for the boundary value problems of a class of fourth-order difference equations.In Chapter 3, we provide various sets of sufficient conditions on the existence of solutions of the boundary value problems when the nonlinearity is superlinear, sublin-ear and Lipschitz.In Chapter 4, when the nonlinear function of the equation is odd for the sec-ond variable, multiple solutions for the boundary value problems of the fourth-order difference equations is obtained via Clark theorem.