Homoclinic solutions for nonautonomous second order Hamiltonian systems with a coercive potential. (English) Zbl 1118.37032
Summary: We are concerned with the existence of homoclinic solutions for the second-order Hamiltonian , where and . A potential is -periodic in , coercive in and the integral of over is equal to 0. A function is continuous, bounded, square integrable and . We will show that there exists a solution such that and , as . Although is not a solution of our system, we are to call a homoclinic solution. It is obtained as a limit of -periodic orbits of a sequence of the second-order differential equations.
|37J45||Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods|
|34C37||Homoclinic and heteroclinic solutions of ODE|
|58E05||Abstract critical point theory|