no. 1
Subharmonic solutions of a nonconvex noncoercive hamiltonian system
RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 1, pp. 27-37

In this paper we study the existence of subharmonic solutions of the hamiltonian system

Jx ˙+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.

@article{RO_2004__38_1_27_0,
     author = {Kallel, Najeh and Timoumi, Mohsen},
     title = {Subharmonic solutions of a nonconvex noncoercive hamiltonian system},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {27--37},
     year = {2004},
     publisher = {EDP Sciences},
     volume = {38},
     number = {1},
     doi = {10.1051/ro:2004010},
     mrnumber = {2083970},
     zbl = {1108.34034},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro:2004010/}
}
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
SP  - 27
EP  - 37
VL  - 38
IS  - 1
PB  - EDP Sciences
UR  - https://www.numdam.org/articles/10.1051/ro:2004010/
DO  - 10.1051/ro:2004010
LA  - en
ID  - RO_2004__38_1_27_0
ER  - 
%0 Journal Article
%A Kallel, Najeh
%A Timoumi, Mohsen
%T Subharmonic solutions of a nonconvex noncoercive hamiltonian system
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2004
%P 27-37
%V 38
%N 1
%I EDP Sciences
%U https://www.numdam.org/articles/10.1051/ro:2004010/
%R 10.1051/ro:2004010
%G en
%F RO_2004__38_1_27_0
Kallel, Najeh; Timoumi, Mohsen. Subharmonic solutions of a nonconvex noncoercive hamiltonian system. RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 1, pp. 27-37. doi: 10.1051/ro:2004010

[1] C. Conley and E. Zehnder, Subharmonic solutions and Morse theory. Phys. A 124 (1984) 649-658. | Zbl | MR

[2] I. Ekeland and H. Hofer, Subharmonics for convex nonautonomous Hamiltonian systems. Commun. Pure Appl. Math. 40 (1987) 1-36. | Zbl | MR

[3] A. Fonda and A.C. Lazer, Subharmonic solutions of conservative systems with nonconvex potentials. Proc. Am. Math. Soc. 115 (1992) 183-190. | Zbl | MR

[4] F. Fonda and M. Willem, Subharmonic oscllations of forced pendulum-type equation J. Differ. Equations 81 (1989) 215-220. | Zbl | MR

[5] G. Fournier, M. Timoumi and M. Willem, The limiting case for strongly indefinite functionals. Topol. Meth. Nonlinear Anal. 1 (1993) 203-209. | Zbl | MR

[6] F. Giannoni, Periodic Solutions of Dynamical Systems by a Saddle Point Theorem of Rabinowitz. Nonlinear Anal. 13 (1989) 707-7019. | Zbl | MR

[7] P.H. Rabinowitz, On Subharmonic Solutions of Hamiltonian Systems. Commun. Pure Appl. Math. 33 (1980) 609-633. | Zbl | MR

[8] M. Timoumi, Subharmonics of convex noncoercive Hamiltonian systems. Coll. Math. 43 (1992) 63-69. | Zbl | MR

[9] M. Willem, Subharmonic oscillations of convex Hamiltonian systems. Nonlinear Anal. 9 (1985) 1311. | Zbl | MR

Cité par Sources :