Existence Of Solutions Of Boundary Value Problems For A Fourth-Order High-dimensional Difference Equations

This dissertation mainly concerns with the existence and multiplicity of solutionsof boundary value problems for a class of fourth-order high dimensional differenceequations. First, we establish a suitable variational functional,and reduces the problemof finding solutions of the boundary value problem to that of seeking critical points ofthe corresponding functional. Then, we obtain the nonexistence and existence resultsof critical points of the variational functional by using critical point theory, and thusa sets of sufficient conditions on the nonexistence and existence of solutions for theboundary value problems of the fourth-order high-dimensional difference equationsare established. This dissertation is composed of four chapters.In Chapter 1, we concentrates on the brief introduction of historic backgroundand significance for all investigated problems, preliminaries, known results and ourmain works.In Chapter 2, we establish the corresponding variational functional and devote tothe study of the nonexistence of nontrivial solutions for the boundary value problemsof the fourth-order high dimensional difference equations.In Chapter 3, by using critical point theory, we consider the existence of solutionsof the boundary value problems when the nonlinearity is superlinear, sublinear andLipschitz.In Chapter 4, by applying the critical point theory, we consider the existenceof solutions of boundary value problem for a class of non-linear fourth-order highdimensional difference equations with nonhomogeneous boundary condition.