Subharmonic solutions of a nonconvex noncoercive hamiltonian system

Najeh Kallel; Mohsen Timoumi

RAIRO - Operations Research - Recherche Opérationnelle (2004)

  • Volume: 38, Issue: 1, page 27-37
  • ISSN: 0399-0559

Abstract

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

How to cite

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Kallel, Najeh, and Timoumi, Mohsen. "Subharmonic solutions of a nonconvex noncoercive hamiltonian system." RAIRO - Operations Research - Recherche Opérationnelle 38.1 (2004): 27-37. <http://eudml.org/doc/245563>.

@article{Kallel2004,
abstract = {In this paper we study the existence of subharmonic solutions of the hamiltonian system\[ \hspace*\{-34.1433pt\}J\dot\{x\}+ u^* \nabla G(t,u(x)) =e(t) \]where $u$ is a linear map, $G $ is a $ C^1$-function and $e$ is a continuous function.},
author = {Kallel, Najeh, Timoumi, Mohsen},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {subharmonic solutions; Hamiltonian system},
language = {eng},
number = {1},
pages = {27-37},
publisher = {EDP-Sciences},
title = {Subharmonic solutions of a nonconvex noncoercive hamiltonian system},
url = {http://eudml.org/doc/245563},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Kallel, Najeh
AU - Timoumi, Mohsen
TI - Subharmonic solutions of a nonconvex noncoercive hamiltonian system
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 1
SP - 27
EP - 37
AB - In this paper we study the existence of subharmonic solutions of the hamiltonian system\[ \hspace*{-34.1433pt}J\dot{x}+ u^* \nabla G(t,u(x)) =e(t) \]where $u$ is a linear map, $G $ is a $ C^1$-function and $e$ is a continuous function.
LA - eng
KW - subharmonic solutions; Hamiltonian system
UR - http://eudml.org/doc/245563
ER -

References

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  1. [1] C. Conley and E. Zehnder, Subharmonic solutions and Morse theory. Phys. A 124 (1984) 649-658. Zbl0605.58015MR759212
  2. [2] I. Ekeland and H. Hofer, Subharmonics for convex nonautonomous Hamiltonian systems. Commun. Pure Appl. Math. 40 (1987) 1-36. Zbl0601.58035MR865356
  3. [3] A. Fonda and A.C. Lazer, Subharmonic solutions of conservative systems with nonconvex potentials. Proc. Am. Math. Soc. 115 (1992) 183-190. Zbl0752.34027MR1087462
  4. [4] F. Fonda and M. Willem, Subharmonic oscllations of forced pendulum-type equation J. Differ. Equations 81 (1989) 215-220. Zbl0708.34028MR1016079
  5. [5] G. Fournier, M. Timoumi and M. Willem, The limiting case for strongly indefinite functionals. Topol. Meth. Nonlinear Anal. 1 (1993) 203-209. Zbl0817.58006MR1233091
  6. [6] F. Giannoni, Periodic Solutions of Dynamical Systems by a Saddle Point Theorem of Rabinowitz. Nonlinear Anal. 13 (1989) 707-7019. Zbl0729.58044MR998515
  7. [7] P.H. Rabinowitz, On Subharmonic Solutions of Hamiltonian Systems. Commun. Pure Appl. Math. 33 (1980) 609-633. Zbl0425.34024MR586414
  8. [8] M. Timoumi, Subharmonics of convex noncoercive Hamiltonian systems. Coll. Math. 43 (1992) 63-69. Zbl0785.58040MR1214224
  9. [9] M. Willem, Subharmonic oscillations of convex Hamiltonian systems. Nonlinear Anal. 9 (1985) 1311. Zbl0579.34030MR813660

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