Applications Of Variational Methods To Second-order Hamiltonian Systems

In this thesis,we investigate the existence of homoclinic orbits of second-orderHamiltonian systems by variational methods and analysis methods.In chapter 1,we introduce the recent development of the problems and consider the historical background.Moreover,we present some preliminary lemmas and definitions.In chapter 2,we study the existence of homoclinic orbits for the second-order periodic Hamiltonian systemsü(t)+?V(t,u(t))=f(t)We prove the existence of homoclinic orbits for the second-order periodic Hamiltonian systems when the potential is superquadratic.In chapter 3,we study the existence of homoclinic orbits for the second-order non-periodic Hamiltonian systemsü(t)-L(t)u(t)+?W(t,u(t))=f(t)We prove the existence of homoclinic orbits for the second-order non-periodic Hamiltonian systems when the potential is superquadratic.And we prove the existence of homoclinic orbits for the second-order non-periodic Hamiltonian systems when L(t)=0 and the potential is not superquadratic.