An approximative method of finding almost homoclinic solutions for Hamiltonian systems

In this lecture, we shall be concerned with the existence of almost homoclinic solutions for Hamiltonian systems. Namely, a certain approximative method of finding almost homoclinic solutions for a class of second order Hamiltonian systems will be described. By the use of this method, an almost homoclinic solution is obtained as a limit of periodic solutions of a sequence of second order differential equations. Finally, an example of a variational nature will be given.