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

In this paper, the periodic solutions of three kind nonautonomous second-order Hamiltonian systems are studied through the least action principle 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 systemswhere B is a antisymmetric matrix, ||B||＜2π/T, and some existence theorems are obtained by appropriate restrictions on F and (?). In Chapter 3, the existence of the odd or even periodic solutions of nonautonomous second-order Hamiltonian systemsand are discussed, and some existence theorems also are presented by appropriate restrictions on F,(?) and p(t). In these conclusions, someare extension and improvement of previous literature, the other are new results.