Study On Periodic Solutions Of Second Order Hamiltonian Systems With Perturbations

Hamiltonian system is a very important field of non-linear functional analysis.It widely exists not only in mathematical science,but also in life science and other scientific fields.Hamiltonian systems(or their perturbation systems)often appear in the form of many scientific fields.Therefore,the study of Hamiltonian systems has very important theoretical value and practical significance.This paper considers the existence of periodic solutions for three kinds of secondorder nonautomous Hamiltonian systems with perturbations.Using the principle of the Saddle Point Theorem and Mountain Pass Theorem,under four different solvable conditions,we improve the results of previous literatures,and we obtain the existence of periodic solutions for four perturbed systems(see chapters 2 and 3,respectively).This paper is divided into three parts.The chapter 1 briefly introduces the background of historical research and the current research situation of Hamiltonian systems,as well as the research content and innovation of this paper.The chapter 2 proves the existence result of periodic solutions of second order Hamiltonian systems with perturbations using the Saddle Point Theorem.The chapter 3 proves the existence result of periodic solutions of second order Hamiltonian systems with perturbations using the Mountain Pass Theorem under classical and local super-quadratic conditions respectively.