In this paper we prove the existence of at least one homoclinic solution for a second order Lagrangian system, where the potential is an almost periodic function of time. This result generalizes existence theorems known to hold when the dependence on time of the potential is periodic. The method is of a variational nature, solutions being found as critical points of a suitable functional. The absence of a group of symmetries for which the functional is invariant (as in the case of periodic potentials) is replaced by the study of problems ''at infinity'' and a suitable use of a property introduced by E. Sere.

On the existence of homoclinic solutions for almost periodic second order systems / E. Serra, M. Tarallo, S. Terracini. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 13:6(1996), pp. 783-812.

On the existence of homoclinic solutions for almost periodic second order systems

M. Tarallo
Secondo
;
1996

Abstract

In this paper we prove the existence of at least one homoclinic solution for a second order Lagrangian system, where the potential is an almost periodic function of time. This result generalizes existence theorems known to hold when the dependence on time of the potential is periodic. The method is of a variational nature, solutions being found as critical points of a suitable functional. The absence of a group of symmetries for which the functional is invariant (as in the case of periodic potentials) is replaced by the study of problems ''at infinity'' and a suitable use of a property introduced by E. Sere.
Settore MAT/05 - Analisi Matematica
http://www.numdam.org/item?id=AIHPC_1996__13_6_783_0
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/175738
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