Existence Of Periodic Solutions For Two Classes Of Second Order Hamiltonian Systems

Recently, second order Hamiltonian systems have attracted a lot of attention for their wide practical background?Especially, the problem of the existence of periodic solutions for second order Hamiltonian systems has developed rapidly in the last 20 years. In this paper, we use the least action principle and the saddle point theorem to study the existence of periodic solutions for two classes of second order Hamiltonian systems and we also obtain several new results.In chapter 1, we briefly introduce the research background of Hamiltonian systems and the main work of the paper.In chapter 2, we mainly discuss the problem of the existence of periodic solutions for second order Hamiltonian systemsWe finally obtain the results under the help of the least action principle and the saddle point theorem.In chapter 3, we research the problem of the existence of periodic solutions for second order discrete Hamiltonian systemsby using the least action principle and the saddle point theorem. Ultimately, the conclusions extend the existing relevant results. Finally, we list several examples to illustrate the main results.