Multiple homoclinic orbits for a class of Hamiltonian systems

被引：0
|
作者：
Eric Paturel
机构：
[1] CEREMADE,
[2] UMR CNRS 7534,undefined
[3] Université Paris-Dauphine,undefined
[4] Place du Maréchal de Lattre de Tassigny,undefined
[5] F-75775 Paris Cedex 16,undefined
[6] France (e-mail: paturel@pi.ceremade.dauphine.fr) ,undefined
来源：
Calculus of Variations and Partial Differential Equations | 2001年 / 12卷
关键词：
Variational Method; Hamiltonian System; Homoclinic Orbit; Relative Category; Multiplicity Result;
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摘要：
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.
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页码：117 / 143
页数：26
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