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October  1997, 3(4): 579-590. doi: 10.3934/dcds.1997.3.579

Periodic and homoclinic solutions for a class of unilateral problems

Samir Adly 1, , Daniel Goeleven 2, and  Dumitru Motreanu 3,

1. 

Institut d'Ingénierie Informatique de Limoges and LACO, URA-1586, 123 Avenue A. Thomas, 87060 Limoges Cedex, France
2. 

Lehrstuhl C für Mathematik R.W.T.H. Aachen, Germany
3. 

Universitatea Al. I. Cuza, BD Copou 11, RO-6600 IASI, Romania

Received  February 1997 Revised  April 1997 Published  July 1997

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: nonconvex energy functional, Hamiltonian system., homoclinic orbit, Critical point theory, calculus of variation for nondifferentiable functions.
Mathematics Subject Classification: 49J40, 49J52, 35J2.
Citation: Samir Adly, Daniel Goeleven, Dumitru Motreanu. Periodic and homoclinic solutions for a class of unilateral problems. Discrete and Continuous Dynamical Systems, 1997, 3 (4) : 579-590. doi: 10.3934/dcds.1997.3.579
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