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Subharmonic solutions of a nonconvex noncoercive Hamiltonian system

Published online by Cambridge University Press:  15 April 2004

Najeh Kallel  and
Mohsen Timoumi
Najeh Kallel
Affiliation:
Institut préparatoire des Études d'ingénieurs de Sfax, Département de Mathématiques, BP 805, CP 3018, Tunisia.
Mohsen Timoumi
Affiliation:
Faculté des sciences de Monastir, Département de Mathématiques, CP 5000, Tunisia; [email protected].
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Abstract

In this paper we study the existence of subharmonic solutions of the Hamiltonian system $$ J\dot x+ u^* \nabla G(t,u(x)) =e(t)$$ where u is a linear map, G is a C 1-function and e is a continuous function.

Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 1 , January 2004 , pp. 27 - 37
Copyright
© EDP Sciences, 2004

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References

Conley, C. and Zehnder, E., Subharmonic solutions and Morse theory. Phys. A 124 (1984) 649-658. CrossRef
Ekeland, I. and Hofer, H., Subharmonics for convex nonautonomous Hamiltonian systems. Commun. Pure Appl. Math. 40 (1987) 1-36. CrossRef
Fonda, A. and Lazer, A.C., Subharmonic solutions of conservative systems with nonconvex potentials. Proc. Am. Math. Soc. 115 (1992) 183-190. CrossRef
F. Fonda and M. Willem, Subharmonic oscllations of forced pendulum-type equation J. Differ. Equations 81 (1989) 215-220.
Fournier, G., Timoumi, M. and Willem, M., The limiting case for strongly indefinite functionals. Topol. Meth. Nonlinear Anal. 1 (1993) 203-209. CrossRef
Giannoni, F., Periodic Solutions of Dynamical Systems by a Saddle Point Theorem of Rabinowitz. Nonlinear Anal. 13 (1989) 707-7019. CrossRef
Rabinowitz, P.H., Subharmonic Solutions, On of Hamiltonian Systems. Commun. Pure Appl. Math. 33 (1980) 609-633. CrossRef
Timoumi, M., Subharmonics of convex noncoercive Hamiltonian systems. Coll. Math. 43 (1992) 63-69.
Willem, M., Subharmonic oscillations of convex Hamiltonian systems. Nonlinear Anal. 9 (1985) 1311.