Study On Periodic Solutions Of Second Order Hamiltonian Systems

This paper considers the existence and multiplicity of periodic solutions about three different second order nonautomous Hamiltonian systems.Using Minimax meth-ods,under new condition,we improve the previous results occuring in paper^[1],^[3],^[4]and^[6]?see chapter 2?,and we obtain two new results which are different from pa-per^[7]?see chapter 3,chapter 4?.This paper is divided into four parts.The chapter 1 briefly introduces the back-ground knowledge and preparation knowledge for Hamiltonian systems.The chapter2 provides the existence result and the multiplicity results about periodic solutions of Hamiltonian systems using the least action principle and the local rinking theorem.The chapter 3 proves the existence result of periodic solutions of asympotically linear Hamiltonian systems using the saddle point theorem.The chapter 4 proves the multi-plicity solutions of superquadratic Hamiltonian systems using the fountain theorem.