Order And The Existence Of Periodic Solutions Of Hamiltonian Systems With P-laplace Operator,

The periodic solutions of Hamiltonian systems are studied by variational methods in this paper. This dissertation is divided into four chapters. The main contents are as follows:Firstly, the source, applications and its research direction of Hamiltonian systems are introduced in Chapter 1, and it also introduces main works and innovative contents;In Chapter 2, some basic knowledge and necessary theorems of Hamiltonian system are described.In Chapter 3, the existence of periodic solutions for n-dimension Duffing system are proved in sublinear potential condition and linear potential condition by using the least action principle and the saddle point theorem. And then three new solvable conclusions are obtained which are some powerful judge conditions to determine the Hamiltonian systems that there are some solutions or not.In Chapter 4, it is firstly considered that the existence of periodic solutions for the second order Hamiltonian system with a p-Laplacian operator under the "subquadratic" potential condition, and then it is also studied that the existence of periodic solutions of Hamiltonian system where A=0 by using the Generalized Mountain Pass Lemma.