Study On Solutions Of Hamiltonian Systems

This paper considers the existence and multiplicity of periodic solutions about two different second order nonautomous Hamiltonian systems.Using Minimax methods,under new condition,we improve the previous results,and we obtain new results(see chapter 2 and chapter 3).This paper is divided into three parts.The chapter 1 briefly introduces the background knowledge and preparation knowledge for Hamiltonian systems.The chapter 2 provides the existence result and the multiplicity results about periodic solutions of Hamiltonian systems with mixed conditions using the Saddle Point Theorem and Symmetric Mountain Pass Theorem.The chapter 3 proves the multiplicity result of periodic solutions of local subquadratic Hamiltonian systems using the Symmetric Mountain Pass Theorem.