Multiple homoclinic orbits for a class of conservative systems

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1. [1] A. Ambrosetti, Critical points and nonlinear variational problems, Mem. Soc. Math. France, 120, No. 49 (1992). Zbl0766.49006MR1164129
2. [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. Zbl0804.34046MR1190931
3. [3] A. Ambrosetti - V. COTI ZELATI, Multiplicté des orbites homoclines pour des systémes conservatifs, Compte RendusAcad. Sci. Paris, 314 (1992), pp. 601-604. Zbl0780.49008MR1158744
4. [4] A. Ambrosetti - V. COTI ZELATI - I. EKELAND, Symmetry breaking in Hamiltonian systems, J. Diff. Equat., 67 (1987), pp. 165-184. Zbl0606.58043MR879691
5. [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. Zbl0492.70018MR647065
6. [6] A. Bahri - H. Berestycki, A perturbation method in critical point theory and applications, Trans. Amer. Math. Soc., 267 (1981), pp. 1-32. Zbl0476.35030MR621969
7. [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. Zbl0549.58019MR728558
8. [8] V. Coti Zelati - I. Ekeland - E. Seré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann., 288 (1990), pp. 133-160. Zbl0731.34050MR1070929
9. [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. Zbl0744.34045MR1119200
10. [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. Zbl0449.70014MR592293
11. [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. Zbl0702.34039MR1079873
12. [12] V.K. Melnikov, On the stability of the center for periodic perturbations, Trans. Moscow Math. Soc., 12 (1963), p. 1-57. Zbl0135.31001MR156048
13. [13] R. Palais - S. SMALE, A generalized Morse theory, Bull. Amer. Math. Soc., 70 (1964), p. 165-171. Zbl0119.09201MR158411
14. [14] H. Poincaré, Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, Paris (1897-1899). JFM25.1847.03
15. [15] P.H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proceed. Royal Soc. Edinburgh, 114-A (1990), pp. 33-38. Zbl0705.34054MR1051605
16. [16] P.H. Rabinowitz - K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Zeit., to appear. Zbl0707.58022MR1095767
17. [17] E. Seré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z., 209 (1992), pp. 27-42. Zbl0725.58017MR1143210
18. [18] E. Seré, Homoclinic orbits on compact hypersurfaces in R2N of restricted contact type, preprint CEREMADE, 1992. 
19. [19] K. Tanaka, Homoclinic orbits in a first order superquadratic Hamiltonian system: convergence of subharmonic orbits, to appear. Zbl0787.34041MR1137618

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