Second-order Non-autonomous Hamiltonian System Cycle Solution Existence,

In this paper, the periodic solutions of two kind nonautonomous second-order Hamiltonian systems and ordinary p-Laplacian system are studied through the least action principle and local linking theorem, saddle point theorem and mountain pass theorem in variational methods, and some sufficient conditions are obtained.As the introduction, in Chapter 1, the principle of the calculus of variations and it's application to Hamiltonian systems is introduced, some essential definitions,relative conclusions and preliminary theorems concerning variational methods are briefly adressed.In Chapter 2, we discuss the existence of the periodic solutions of nonautonomous second-order Hamiltonian systems where A(t) is a symmetric matrix and every element of A(t) is a continuous function concerned with t in [0,T], and some existence theorems are obtained by appropriate restrictions on F,▽F and A(t).In Chapter 3, the existence of periodic solutions of nonautonomous second-order Hamiltonian systems are discussed, and some existence theorems also are presented by appropriate restrictions on F,▽F and f(t).In Chapter 4, the existence of periodic solutions of ordinary p-Laplacian systems existence theorems also are presented by mountain pass lemma. In these conclusions, some are extension and improvement of previous literature, the other are new results.