Periodic Solutions Of Second Order Non-autonomous Hamiltonian Systems

In this dissertation, we study the periodic solutions of three kinds nonautonomous second-order Hamiltonian systems by using the least action principle and saddle point, and some sufficient conditions are obtained. This dissertation is divided into four chapters, the main contents are as follows:In Chapter1, we sketch the historical background, the up-to-date progress for all the investigated problems together with preliminary tools and our main work in this dissertation.In Chapter2, by using the least action principle, we study the existence of periodic solutions for the second-order Hamiltonian system At first, under the subconvex condition, some existence theorems of periodic solutions are ob-tained, then some existence theorems of periodic solutions are obtained in sublinear potential condition and convex condition.In Chapter3, the existence of periodic solutions of nonautonomous second-order Hamil-tonian systems are discussed by using the saddle point theorem, and some existence theorems are presented by appropriate restrictions on F, VFand A.In Chapter4, we discuss the existence of periodic solutions for the second-order Hamil-tonian system with forcing term by using the saddle point theorem, and some new solvable conclusions are obtained.