Critical Point Theory And Its Application On Second Order Hamiltonian Systems

This paper considers some periodic solution results for two class second order nonautonomous Hamiltonian systems.For the first class,it considers periodic solutions for a class of second order superquadratic systems.Using Linking Theorem and Fountain Theorem the existence and multiplicity of periodic solutions are obtained.For the second class,it mainly studies on impact Hamiltonian systems with new sublinear conditions,and in order to obtain the multiplicity of nontrivial periodic bouncing solutions for the system,we prove a Generalized Nonsmooth Saddle Point Theorem.This paper is divided into four chapters.In the first chapter,we briefly introduce the research background for Hamiltonian system,summarize the main results in this field and give the main topic we will study on in this paper.In the second chapater,we give some basic knowledge and prove the Generalized Nonsmooth Saddle Point Theorem.In the third chapter,the existence and multiplicity of periodic solutions for second order Hamiltonian systems with new superquadratic conditions are obtained.And in the last chapter,we obtain the multiplicity of nontrivial periodic bouncing solutions for the impact system.