Periodic Solutions For Higher Order Laplacian Difference Equations Containing Both Advances And Retardations

In this dissertation,we mainly consider the existence of periodic solutions for higher order nonlinear difference equations containing both many advances and retardations.By establishing a corresponding variational framework,the problem of the existence of the periodic solution of the difference equation is transformed into the existence problem of the corresponding functional critical point.Then we use the Linking Theorem to obtain the existence of the critical point of the functional,and then obtain the existence and multiplicity of the periodic solution under different conditions.This dissertation includes three chapters,the main contents are as follows:The first chapter briefly discusses the historical background,research signifi-cance and research progress of the issues discussed in this paper.At the same time,for the convenience of the reader,the relevant basic conclusions and preliminary knowledge are given.In chapter 2,we consider a 29)th-order nonlinear difference equation contain-ing both many advances and retardations with_{?8?-Laplacian.Using the Linking Theorem,we obtain some new and concrete criteria for the existence and mul-tiplicity of periodic and subharmonic solutions in the more general case of the nonlinearity.In chapter 3,we consider a 29}th-order nonlinear difference equation contain-ing both many advances and retardations with-Laplacian.Using the Linking Theorem,we obtain some new and concrete criteria for the existence and multi-plicity of periodic and subharmonic solutions.