Periodic and homoclinic solutions for a class of unilateral problems

Samir Adly; Daniel Goeleven; Dumitru Motreanu

doi:10.3934/dcds.1997.3.579

Article Contents

1997, Volume 3, Issue 4: 579-590. Doi: 10.3934/dcds.1997.3.579

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Periodic and homoclinic solutions for a class of unilateral problems

1.
Institut d'Ingénierie Informatique de Limoges and LACO, URA-1586, 123 Avenue A. Thomas, 87060 Limoges Cedex
2.
Lehrstuhl C für Mathematik R.W.T.H. Aachen
3.
Universitatea Al. I. Cuza, BD Copou 11, RO-6600 IASI

Received: February 1997

Revised: April 1997

Published: October 1997

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Abstract

This paper contains some existence and multiplicity results for periodic solutions of second order nonautonomous and nonsmooth Hamiltonian systems involving nonconvex superpotentials. This study is achieved by proving the existence of homoclinic solutions. These solutions are constructed as critical points of the corresponding nonconvex and nonsmooth energy functional.

Keywords:

Critical point theory,
nonconvex energy functional,
calculus of variation for nondifferentiable functions,
homoclinic orbit,
Hamiltonian system.

Mathematics Subject Classification: 49J40, 49J52, 35J20.

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