Subharmonic solutions of a nonconvex noncoercive Hamiltonian system

Najeh Kallel; Mohsen Timoumi

RAIRO - Operations Research (2010)

  • 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 C1-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 38.1 (2010): 27-37. <http://eudml.org/doc/105300>.

@article{Kallel2010,
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 C1-function and e is a continuous function. },
author = {Kallel, Najeh, Timoumi, Mohsen},
journal = {RAIRO - Operations Research},
keywords = {subharmonic solutions; Hamiltonian system},
language = {eng},
month = {3},
number = {1},
pages = {27-37},
publisher = {EDP Sciences},
title = {Subharmonic solutions of a nonconvex noncoercive Hamiltonian system},
url = {http://eudml.org/doc/105300},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Kallel, Najeh
AU - Timoumi, Mohsen
TI - Subharmonic solutions of a nonconvex noncoercive Hamiltonian system
JO - RAIRO - Operations Research
DA - 2010/3//
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 $$ J\dot x+ u^* \nabla G(t,u(x)) =e(t) $$ where u is a linear map, G is a C1-function and e is a continuous function.
LA - eng
KW - subharmonic solutions; Hamiltonian system
UR - http://eudml.org/doc/105300
ER -

References

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  1. C. Conley and E. Zehnder, Subharmonic solutions and Morse theory. Phys. A124 (1984) 649-658.  
  2. I. Ekeland and H. Hofer, Subharmonics for convex nonautonomous Hamiltonian systems. Commun. Pure Appl. Math.40 (1987) 1-36.  
  3. A. Fonda and A.C. Lazer, Subharmonic solutions of conservative systems with nonconvex potentials. Proc. Am. Math. Soc.115 (1992) 183-190.  
  4. F. Fonda and M. Willem, Subharmonic oscllations of forced pendulum-type equation J. Differ. Equations81 (1989) 215-220.  
  5. G. Fournier, M. Timoumi and M. Willem, The limiting case for strongly indefinite functionals. Topol. Meth. Nonlinear Anal.1 (1993) 203-209.  
  6. F. Giannoni, Periodic Solutions of Dynamical Systems by a Saddle Point Theorem of Rabinowitz. Nonlinear Anal.13 (1989) 707-7019.  
  7. P.H. Rabinowitz, On Subharmonic Solutions of Hamiltonian Systems. Commun. Pure Appl. Math.33 (1980) 609-633.  
  8. M. Timoumi, Subharmonics of convex noncoercive Hamiltonian systems. Coll. Math.43 (1992) 63-69.  
  9. M. Willem, Subharmonic oscillations of convex Hamiltonian systems. Nonlinear Anal.9 (1985) 1311.  

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