Existence Of Periodic Solutions For Second-Order Discrete Hamilton Systems

This Master’s thesis mainly applies the variational method to study second-order discrete Hamiltonian systems.By seeking the critical point of the corre-sponding functional of the system,the existence and multiplicity of periodic solu-tions of the system are obtained.The full text of this thesis is divided into four chapters:In Chapter 1,we briefly summarizes the historical background of this topic,together with some research status,and the main achievements of the discrete Hamiltonian systems.In Chapter 2,we provide some preliminary knowledge needed in this thesis.In Chapter 3,Study the existence of the following second order discrete Hamil-tonian systems(?)Firstly,the variational framework of the studied system is established,and the relevant lemmas are given.Then,the existence of periodic solutions for second order discrete Hamiltonian systems is proved using the minimum action principle and saddle point theorem,which generalizes the existing work.In Chapter 4,Study the multiplicity of the following second order discrete Hamiltonian systems(?)Firstly,the variational framework of the system under study is established,and the relevant lemmas are given.Then,using the minimax method,the multiplicity problem of periodic solutions for second order discrete Hamiltonian systems is proved,and new conclusions are obtained.