The Study On Homoclinic Solutions For Several Classes Of Second Order Hamiltonian Systems

In this thesis,we study the existence of multiple homoclinic solutions for a class of second order Hamiltonian systems.The thesis consists of three chapters.In chapter one,we first introduce the origin and development of the study on homocinic solu-tions for Hamiltonian systems and then describe the development of famous variational methods for this kind of problems.After that we present the issues that we focus on and we give our main results.In chapter two,we prove the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems whose potential function is superquadratic at infinity.In chapter three,we investigate the multiplicity of homoclinic solutions for a class of second order Hamiltonian systems whose potential function is only defined near the origin.Actually we prove that it possess a sequence of homoclinic solutions which converges to the origin under the assumption that the potential function satisfies some kind of growth condition near the origin.