Abstract
In recent years, starting with works of Bolotin [Bol], Coti-Zelati, Ekeland and Sere [CZES], Coti-Zelati & Rabinowitz [CZR1], [CZR2], Rabinowitz [Ra4], variational methods have been applied to study the existence of homoclinic and heteroclinic solutions of second-order equations and Hamiltonian systems. The search for homoclinic and heteroclinic solutions is a classical problem, originated from the work of Poincare and has been developed from several points of view. Existence of homoclinic solutions can be obtained by analyzing the intersection properties of the stable and unstable manifolds of the fixed points. There is a standard method to find infinitely nearby homoclinics provided that the stable and unstable manifolds of a fixed point intersect transversally. For this approach we refer the reader to Moser [Mo], Guckenheimer & Holmes [GH], Wiggins [Wig].
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