Applications Of Critical Point Theory To Second Order Hamiltonian Systems

In this thesis, the periodic solutions of some nonautonomous second-order Hamilton systems with suitable conditions are studied through the least action principle and minimax theorems in variational methods.Chapter 1 is devoted to the evolution and development of the principle of the Calculus of Variations and the problems that will be studied are presented.In Chapter 2, some essential definitions and preliminary theorems concerning variational methods are introduced.In Chapter 3, we present some applications of the least principle on second-order Hamilton systems. We introduce the results obtained by the least action principle and the study of the transformation of the periodic solutions of second order systems to the solutions of the corresponding Euler equation. We systematically introduce some results obtained by the least action principle or by the combination of the least action principle and some other theorems. And the periodic solutions of some nonautonomous second-order Hamilton systems are studied with the nonlinearity satisfying the sublinear conditions.Chapter 4 is devoted to the applications of the minimax principle on second-order Hamilton systems: introducing the saddle point theorem and some other minimax methods and some rencent results are obtained by minimax medthods. In this chapter, the saddle point theorem is mainly used to the studies of periodic solutions of some class of second-order Hamilton systems.