Anti-periodic Solutions Of Discrete Hamiltonian Systems

By using the dual least action principle and the perturbation technique, the antiperiodic solutions are investigated in this paper for a second order nonlinear difference system and a discrete system with p-Laplacian.In chapter 1, we introduce the history of the calculus of variation and the critical point theorem. A summary is presented for the study of difference equations via variational approach. And, we give the main research contents of this paper.In chapter 2, we recall some notations and some well known fundamental lemmas of the critical point theorem.In chapter 3, we study a second order nonlinear difference equation with antiperiodic boundary conditionWe construct the variational structure and the solvability of the problem correspond to the existence of critical points of the functional. Then, by using the dual least action principle and the perturbation technique, the existence results are given under some sufficient conditions upon the nonlinear term.In chapter 4, we consider the existence of anti-periodic solutions of the following difference equation with p-laplacian:Firstly, we transform the p-laplacian system into the Hamiltonian system. Then, by using the dual least action principle and the perturbation technique, the existence results are given under some sufficient conditions upon the nonlinear term.At the last chapter the main results of this dissertation are summarized.