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},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {1},
     year = {2004},
     doi = {10.1051/ro:2004010},
     mrnumber = {2083970},
     zbl = {1108.34034},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro:2004010/}
}
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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. http://www.numdam.org/articles/10.1051/ro:2004010/

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

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

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

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

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

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

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

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

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

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