Ambrosetti, Antonio; Coti Zelati, Vittorio
Multiple homoclinic orbits for a class of conservative systems
Rendiconti del Seminario Matematico della Università di Padova, Tome 89 (1993) , p. 177-194
Zbl 0806.58018 | MR 1229052 | 4 citations dans Numdam
URL stable : http://www.numdam.org/item?id=RSMUP_1993__89__177_0

Bibliographie

[1] A. Ambrosetti, Critical points and nonlinear variational problems, Mem. Soc. Math. France, 120, No. 49 (1992). Numdam | MR 1164129 | Zbl 0766.49006

[2] A. Ambrosetti - M.L. Bertotti, Homoclinics for a second order conservative systems, in Partial Differential Equations and Related Subjects, M. Miranda Ed. Longman (1992), pp. 21-37. MR 1190931 | Zbl 0804.34046

[3] A. Ambrosetti - V. COTI ZELATI, Multiplicté des orbites homoclines pour des systémes conservatifs, Compte Rendus Acad. Sci. Paris, 314 (1992), pp. 601-604. MR 1158744 | Zbl 0780.49008

[4] A. Ambrosetti - V. COTI ZELATI - I. EKELAND, Symmetry breaking in Hamiltonian systems, J. Diff. Equat., 67 (1987), pp. 165-184. MR 879691 | Zbl 0606.58043

[5] A. Ambrosetti - G. MANCINI, On a theorem by Ekeland and Lasry concerning the number of periodic Hamiltonian trajectories, J. Diff. Equat., 43 (1982), pp. 249-256. MR 647065 | Zbl 0492.70018

[6] A. Bahri - H. Berestycki, A perturbation method in critical point theory and applications, Trans. Amer. Math. Soc., 267 (1981), pp. 1-32. MR 621969 | Zbl 0476.35030

[7] S.V. Bolotin, The existence of homoclinic motions, Vestnik Moscow Univ. Ser. I, Math. Mekh., 6 (1983), pp. 98-103; Moscow Univ. Math. Bull., 38-6 (1983), pp. 117-123. MR 728558 | Zbl 0549.58019

[8] V. Coti Zelati - I. Ekeland - E. Seré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann., 288 (1990), pp. 133-160. MR 1070929 | Zbl 0731.34050

[9] V. Coti Zelati - P.H. Rabinowitz, Homoclinic orbits for a second order Hamiltonian systems possessing superquadratic potentials, Jour. Am. Math. Soc., 4 (1991), pp. 693-727. MR 1119200 | Zbl 0744.34045

[10] I. Ekeland - J. M. LASRY, On the number of closed trajectories for a Hamiltonian flow on a convex energy surface, Ann. Math., 112 (1980), pp. 283-319. MR 592293 | Zbl 0449.70014

[11] H. Hofer - K. WYSOCKI, First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems, Math. Ann., 288 (1990), pp. 483-503. MR 1079873 | Zbl 0702.34039

[12] V.K. Melnikov, On the stability of the center for periodic perturbations, Trans. Moscow Math. Soc., 12 (1963), p. 1-57. MR 156048 | Zbl 0135.31001

[13] R. Palais - S. SMALE, A generalized Morse theory, Bull. Amer. Math. Soc., 70 (1964), p. 165-171. MR 158411 | Zbl 0119.09201

[14] H. Poincaré, Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, Paris (1897-1899). JFM 25.1847.03

[15] P.H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proceed. Royal Soc. Edinburgh, 114-A (1990), pp. 33-38. MR 1051605 | Zbl 0705.34054

[16] P.H. Rabinowitz - K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Zeit., to appear. MR 1095767 | Zbl 0707.58022

[17] E. Seré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z., 209 (1992), pp. 27-42. MR 1143210 | Zbl 0725.58017

[18] E. Seré, Homoclinic orbits on compact hypersurfaces in R2N of restricted contact type, preprint CEREMADE, 1992.

[19] K. Tanaka, Homoclinic orbits in a first order superquadratic Hamiltonian system: convergence of subharmonic orbits, to appear. MR 1137618 | Zbl 0787.34041