Multiple homoclinic orbits for a class of conservative systems

Antonio Ambrosetti; Vittorio Coti Zelati

Rendiconti del Seminario Matematico della Università di Padova (1993)

  • Volume: 89, page 177-194
  • ISSN: 0041-8994

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Ambrosetti, Antonio, and Coti Zelati, Vittorio. "Multiple homoclinic orbits for a class of conservative systems." Rendiconti del Seminario Matematico della Università di Padova 89 (1993): 177-194. <http://eudml.org/doc/108285>.

@article{Ambrosetti1993,
author = {Ambrosetti, Antonio, Coti Zelati, Vittorio},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {hamiltonians; critical points; homoclinic orbits},
language = {eng},
pages = {177-194},
publisher = {Seminario Matematico of the University of Padua},
title = {Multiple homoclinic orbits for a class of conservative systems},
url = {http://eudml.org/doc/108285},
volume = {89},
year = {1993},
}

TY - JOUR
AU - Ambrosetti, Antonio
AU - Coti Zelati, Vittorio
TI - Multiple homoclinic orbits for a class of conservative systems
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1993
PB - Seminario Matematico of the University of Padua
VL - 89
SP - 177
EP - 194
LA - eng
KW - hamiltonians; critical points; homoclinic orbits
UR - http://eudml.org/doc/108285
ER -

References

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  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
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Citations in EuDML Documents

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  1. Roberto Giambò, Fabio Giannoni, Paolo Piccione, On the multiplicity of brake orbits and homoclinics in Riemannian manifolds
  2. Antonio Ambrosetti, Marino Badiale, Homoclinics : Poincaré-Melnikov type results via a variational approach
  3. Paolo Caldiroli, Margherita Nolasco, Multiple homoclinic solutions for a class of autonomous singular systems in R2
  4. Fabio Giannoni, Louis Jeanjean, Kazunaga Tanaka, Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems
  5. Francesca Alessio, Piero Montecchiari, Multibump solutions for a class of lagrangian systems slowly oscillating at infinity

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