Existence Of Periodic Solutions For Second-order Discrete Hamilton Systems

In this thesis, we consider the existence and multiplicity of periodic solutions for a class of second-order discrete Hamiltonian systems by making use of the minimax methods in critical point theory and obtain some new results. Δ2u(t-1)+▽F(t,u(t))= 0, (?)t∈Z.The thesis is divided into four sections according to the contents.In Chapter 1, it is introduced the researched background of problems and the main work of the paper.In Chapter 2, some essential definitions and preliminary theorems concerning variational methods are introduced.In the third chapter, we presented the variational structure and some lemmas, and then introducing a new subquadratic growth condition and a new quadratic condition to studies the existence of periodic solutions for a class of second-order discrete Hamiltonian systems by making use of the minimax methods in critical point theory. Our theorems generalized and improves some known results in the literature.In chapter 4, we presented the variational structure and some lemmas, and then introducing a new control function to studies the existence of periodic solutions for a class of second-order discrete Hamiltonian systems by making use of the least action principle and the generalized Saddle Point Theorem in variational methods. We obtain some new existence results.