Abstract.
In this paper, we obtain the existence of at least two nontrivial homoclinic orbits for a class of second order autonomous Hamiltonian systems. This multiplicity result is obtained by a new variational method based on the relative category: to overcome the lack of compactness of the problem, we first solve perturbed nonautonomous problems and study the limit of the solutions as the nonautonomous perturbation goes to 0. This method allows to get rid of some assumptions on the potential used in the work of Ambrosetti and Coti-Zelati.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received August 9, 1999 / Accepted September 7, 1999 / Published online September 14, 2000
Rights and permissions
About this article
Cite this article
Paturel, E. Multiple homoclinic orbits for a class of Hamiltonian systems. Calc Var 12, 117–143 (2001). https://doi.org/10.1007/PL00009909
Issue Date:
DOI: https://doi.org/10.1007/PL00009909