Heteroclinic solutions for a class of the second order Hamiltonian systems. (English) Zbl 1117.37033
Summary: We are concerned with the existence of heteroclinic orbits for the second-order Hamiltonian system , where and , . We will assume that and a certain subset satisfy the following conditions. is a set of isolated points and . For every sufficiently small there exists such that for all , if then . The integrals , , are equibounded and , as , uniformly on compact subsets of . Our result states that each point in is joined to another point in by a solution of our system.
|37J45||Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods|
|58E05||Abstract critical point theory|
|34C37||Homoclinic and heteroclinic solutions of ODE|