The Existence Of Second-order Discrete Hamiltonian System Periodic Solution

In this thesis, by using the least action principle and saddle point theorem in variational methods, the following two nonlinear second order discrete Hamiltonian systems are studied.In Chapter 1, it is introduced that the evolution and development of the principle of the Calculus of Variations and its application to Hamiltonian systems. Besides, some reseach results are summed up for discrete Hamiltonian systems.In Chapter 2, some essential definitions and preliminary theorems concerning variational methods are introduced.In Chapter 3, variational structure and some lemmas are pesented, and then by using the least action principle and local linking theorm, some new existence and multiplicity results are obtained for periodic solutions for the following non-antonomous second-order discrete Hamiltonian systems(DHS+).In chapter 4, variational structure and some lemmas are pesented, and then by using saddle point theorm in critical point theory, some existence results are obtained for periodic solutions of the non-antonomous second-order discrete Hamiltonian systems(DHS-), the conclusions are improvement of previous result.