Morse theory and existence of periodic solutions of convex hamiltonian systems
Bulletin de la Société Mathématique de France, Tome 116 (1988) no. 2, pp. 171-197.
@article{BSMF_1988__116_2_171_0,
     author = {Szulkin, Andrzej},
     title = {Morse theory and existence of periodic solutions of convex hamiltonian systems},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {171--197},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {116},
     number = {2},
     year = {1988},
     doi = {10.24033/bsmf.2094},
     mrnumber = {90f:58074},
     zbl = {0669.58004},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/bsmf.2094/}
}
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Szulkin, Andrzej. Morse theory and existence of periodic solutions of convex hamiltonian systems. Bulletin de la Société Mathématique de France, Tome 116 (1988) no. 2, pp. 171-197. doi : 10.24033/bsmf.2094. http://www.numdam.org/articles/10.24033/bsmf.2094/

[1] Aubin (J.P.) and Ekeland (I.). - Applied Nonlinear Analysis. - New York, Wiley, 1984. | MR | Zbl

[2] Berestycki (H.), Lasry (J.M.), Mancini (G.) and Ruf (B.). - Existence of multiple periodic orbits on star-shaped Hamiltonian surfaces, Comm. Pure Appl. Math., t. 38, 1985, p. 253-289. | MR | Zbl

[3] Castro (A.) and Lazer (A.C.). - Critical point theory and the number of solutions of a nonlinear Dirichlet problem, Ann. Mat. Pura Appl. (4), t. 120, 1979, p. 113-137. | MR | Zbl

[4] Chang (K.C.). - Morse theory on Banach spaces and its applications to partial differential equations, Chinese Ann. Math. Ser. B, t. 4, 1983, p. 381-399. | MR | Zbl

[5] Chang (K.C.). - Morse theory and its applications to PDE, [Séminaire de Mathématiques Supérieures] 1983, Université de Montréal, to appear.

[6] Clarke (F.H.) and Ekeland (I.). - Hamiltonian trajectories having prescribed minimal period, Comm. Pure Appl. Math., t. 33, 1980, p. 103-116. | MR | Zbl

[7] Ekeland (I.). - Nonconvex minimization problems, Bull. Amer. Math. Soc., t. 1, 1979, p. 443-474. | MR | Zbl

[8] Ekeland (I.). - Une théorie de Morse pour les systèmes hamiltoniens convexes, Ann. Inst. H. Poincaré Anal. Non Linéaire, t. 1, 1984, p. 19-78. | Numdam | MR | Zbl

[9] Ekeland (I.) and Hofer (H.). - Periodic solutions with presbribed minimal period for convex autonomous hamiltonian systems, Invent. Math., t. 81, 1985, p. 155-188. | MR | Zbl

[10] Ekeland (I.) and Lasry (J.M.). - On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface, Ann. Math., t. 112, 1980, p. 283-319. | MR | Zbl

[11] Ekeland (I.) and Lassoued (L.). - Un flot hamiltonien a au moins deux trajectoires fermées sur toute surface d'énergie convexe et bornée, C. R. Acad. Sci. Paris Sér. I Math., t. 301, 1985, p. 161-164. | MR | Zbl

[12] Ekeland (I.) and Lassoued (L.). - Multiplicité des trajectoires fermées de systèmes hamiltoniens convexes, to appear.

[13] Gromoll (D.) and Meyer (W.). - On differentiable functions with isolated critical points, Topology, t. 8, 1969, p. 361-369. | MR | Zbl

[14] Hofer (H.). - The topological degree at a critical point of mountain pass type, Proc. Sym. Pure Math., to appear.

[15] Landesman (E.M.), Lazer (A.C.) and Meyers (D.R.). - On saddle point problems in the calculus of variations, the Ritz algorithm, and monotone convergence, J. Math. Anal. Appl., t. 52, 1975, p. 594-614. | MR | Zbl

[16] Lang (S.). - Differential Manifolds. - Reading, Mass., Addison-Wesley, 1972. | MR | Zbl

[17] Lassoued (L.) and Viterbo (C.). - La théorie de Morse pour les systèmes hamiltoniens, [Colloque du Ceremade], Hermann, to appear.

[18] Mawhin (J.) and Willem (M.). - On the generalized Morse lemma, Preprint, Université Catholique de Louvain, 1985. | MR

[19] Pitcher (E.). - Inequalities of critical point theory, Bull. Amer. Math. Soc., t. 64, 1958, p. 1-30. | MR | Zbl

[20] Rabinowitz (P.H.). - Variational methods for nonlinear eigenvalue problems, [Proc. Sym. on Eigenvalues of Nonlinear Problems], pp. 143-195. - Rome, Edizioni Cremonese, 1974. | MR

[21] Rabinowitz (P.H.). - Periodic solutions of Hamiltonian systems : a survey, SIAM, J. Math. Anal., t. 13, 1982, p. 343-352. | MR | Zbl

[22] Rothe (E.H.). - Critical point theory in Hilbert space under regular boundary conditions, J. Math. Anal. Appl., t. 36, 1971, p. 377-431. | MR | Zbl

[23] Rothe (E.H.). - Morse theory in Hilbert space, Rocky Moutain, J. Math., t. 3, 1973, p. 251-274. | MR | Zbl

[24] Spanier (E.). - Algebraic Topology. - New York, NcGraw-Hill, 1966. | MR | Zbl

[25] Viterbo (C.). - Une théorie de Morse pour les systèmes hamiltoniens étoilés, Thesis, Université Paris-Dauphine, 1985. | MR

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