@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}, volume = {116}, year = {1988}, pages = {171-197}, doi = {10.24033/bsmf.2094}, mrnumber = {90f:58074}, zbl = {0669.58004}, language = {en}, url = {http://dml.mathdoc.fr/item/BSMF_1988__116_2_171_0} }
Szulkin, Andrzej. Morse theory and existence of periodic solutions of convex hamiltonian systems. Bulletin de la Société Mathématique de France, Tome 116 (1988) pp. 171-197. doi : 10.24033/bsmf.2094. http://gdmltest.u-ga.fr/item/BSMF_1988__116_2_171_0/
[1] Applied Nonlinear Analysis. - New York, Wiley, 1984. | MR 87a:58002 | Zbl 0641.47066
and . -[2] Existence of multiple periodic orbits on star-shaped Hamiltonian surfaces, Comm. Pure Appl. Math., t. 38, 1985, p. 253-289. | MR 86j:58039 | Zbl 0569.58027
, , and . -[3] 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 81d:58022 | Zbl 0426.35038
and . -[4] Morse theory on Banach spaces and its applications to partial differential equations, Chinese Ann. Math. Ser. B, t. 4, 1983, p. 381-399. | MR 85j:58040 | Zbl 0534.58020
. -[5] Morse theory and its applications to PDE, [Séminaire de Mathématiques Supérieures] 1983, Université de Montréal, to appear.
. -[6] Hamiltonian trajectories having prescribed minimal period, Comm. Pure Appl. Math., t. 33, 1980, p. 103-116. | MR 81e:70017 | Zbl 0403.70016
and . -[7] Nonconvex minimization problems, Bull. Amer. Math. Soc., t. 1, 1979, p. 443-474. | MR 80h:49007 | Zbl 0441.49011
. -[8] Une théorie de Morse pour les systèmes hamiltoniens convexes, Ann. Inst. H. Poincaré Anal. Non Linéaire, t. 1, 1984, p. 19-78. | Numdam | MR 85f:58023 | Zbl 0537.58018
. -[9] Periodic solutions with presbribed minimal period for convex autonomous hamiltonian systems, Invent. Math., t. 81, 1985, p. 155-188. | MR 87b:58028 | Zbl 0594.58035
and . -[10] On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface, Ann. Math., t. 112, 1980, p. 283-319. | MR 81m:58032 | Zbl 0449.70014
and . -[11] 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 87e:58040 | Zbl 0588.58013
and . -[12] Multiplicité des trajectoires fermées de systèmes hamiltoniens convexes, to appear.
and . -[13] On differentiable functions with isolated critical points, Topology, t. 8, 1969, p. 361-369. | MR 39 #7633 | Zbl 0212.28903
and . -[14] The topological degree at a critical point of mountain pass type, Proc. Sym. Pure Math., to appear.
. -[15] 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 54 #8403 | Zbl 0354.35004
, and . -[16] Differential Manifolds. - Reading, Mass., Addison-Wesley, 1972. | MR 55 #4241 | Zbl 0239.58001
. -[17] La théorie de Morse pour les systèmes hamiltoniens, [Colloque du Ceremade], Hermann, to appear.
and . -[18] On the generalized Morse lemma, Preprint, Université Catholique de Louvain, 1985. | MR 87k:58051
and . -[19] Inequalities of critical point theory, Bull. Amer. Math. Soc., t. 64, 1958, p. 1-30. | MR 20 #2648 | Zbl 0083.32704
. -[20] Variational methods for nonlinear eigenvalue problems, [Proc. Sym. on Eigenvalues of Nonlinear Problems], pp. 143-195. - Rome, Edizioni Cremonese, 1974. | MR 57 #4232
. -[21] Periodic solutions of Hamiltonian systems : a survey, SIAM, J. Math. Anal., t. 13, 1982, p. 343-352. | MR 83e:58028 | Zbl 0521.58028
. -[22] Critical point theory in Hilbert space under regular boundary conditions, J. Math. Anal. Appl., t. 36, 1971, p. 377-431. | MR 44 #3356 | Zbl 0218.58005
. -[23] Morse theory in Hilbert space, Rocky Moutain, J. Math., t. 3, 1973, p. 251-274. | MR 48 #12594 | Zbl 0281.49027
. -[24] Algebraic Topology. - New York, NcGraw-Hill, 1966. | MR 35 #1007 | Zbl 0145.43303
. -[25] Une théorie de Morse pour les systèmes hamiltoniens étoilés, Thesis, Université Paris-Dauphine, 1985. | MR 87a:58072
. -