Homoclinic orbits for a singular second order hamiltonian system

Kazunaga Tanaka

Annales de l'I.H.P. Analyse non linéaire (1990)

  • Volume: 7, Issue: 5, page 427-438
  • ISSN: 0294-1449

How to cite

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Tanaka, Kazunaga. "Homoclinic orbits for a singular second order hamiltonian system." Annales de l'I.H.P. Analyse non linéaire 7.5 (1990): 427-438. <http://eudml.org/doc/78232>.

@article{Tanaka1990,
author = {Tanaka, Kazunaga},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {singular potential; critical point; minimax argument; homoclinic orbit},
language = {eng},
number = {5},
pages = {427-438},
publisher = {Gauthier-Villars},
title = {Homoclinic orbits for a singular second order hamiltonian system},
url = {http://eudml.org/doc/78232},
volume = {7},
year = {1990},
}

TY - JOUR
AU - Tanaka, Kazunaga
TI - Homoclinic orbits for a singular second order hamiltonian system
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 5
SP - 427
EP - 438
LA - eng
KW - singular potential; critical point; minimax argument; homoclinic orbit
UR - http://eudml.org/doc/78232
ER -

References

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  1. [1] A. Ambrosetti and V. Coti-Zelati, Critical points with lack of compactness and applications to singular dynamical system, Ann Mat. Pura Appl., Vol. 149, 1987, pp. 237-259. Zbl0642.58017MR932787
  2. [2] A. Ambrosetti and V. Coti-Zelati, Periodic solutions of singular dynamical systems, Periodic solutions of Hamiltonian systems and related topics, P. H. RABINOWITZ et al. Eds., V209, NATO ASI Series, Reidel, 1987, pp. 1-10. Zbl0632.34042MR920605
  3. [3] A. Ambrosetti and V. Coti-Zelati, Noncollision orbits for a class of Keplerian-like potentials, Ann. Inst. Henri Poincaré, Analyse non linéaire, Vol. 5, 1988, pp. 287-295. Zbl0667.58055MR954474
  4. [4] A. Bahri and P.H. Rabinowitz, A minimax methods for a class of Hamiltonian systems with singular potentials, J. Funct. Anal., Vol. 82, 1989, pp. 412-428. Zbl0681.70018MR987301
  5. [5] M. Degiovanni, F. Giannoni and A. Marino, Periodic solutions of dynamical systems with Newtonian type potentials, Periodic solutions of Hamiltonian systems and related topics, P. H. RABINOWITZ et al. Eds., V209, NATO ASI Series, Reidel, 1987, pp. 111- 115. Zbl0632.34038MR920613
  6. [6] C. Greco, Periodic solutions of a class of singular Hamiltonian systems, Nonlinear Analysis ; T.M.A., Vol. 12, 1988, pp. 259-269. Zbl0648.34048MR928560
  7. [7] C. Greco, Remarks on periodic solutions for some dynamical systems with singularities, Periodic solutions of Hamiltonian systems and related topics, P. H. RABINOWITZ et al. Eds., V209, NATO ASI Series, Reidel, 1987, pp. 169-173. Zbl0632.34043MR920620
  8. [8] W.B. Gordon, Conservative dynamical systems involving strong forces, Trans. Am. Math. Soc., Vol. 204, 1975, pp. 113-135. Zbl0276.58005MR377983
  9. [9] W. Klingenberg, Lectures on closed geodesics, Grundlehren der Math. Wis.., Vol. 235, Springer-Verlag, Berlin-New York, 1978. Zbl0397.58018MR478069
  10. [10] L.A. Lyusternik and A.I. Fet, Variational problems on closed manifolds, Dokl. Akad. Nauk. U.S.S.R. (N.S.), Vol. 81, 1951, pp. 17-18. Zbl0045.20903MR44760
  11. [11] P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, C.B.M.S. Reg. Conf. Ser. in Math. #65, Am. Math. Soc., Providence, RI, 1986. Zbl0609.58002MR845785
  12. [12] P.H. Rabinowitz, Periodic and heteroclinic orbits for a periodic Hamiltonian system, Ann. Inst. Henri Poincaré, Analyse non linéaire, Vol. 6, 1989, pp. 331-346. Zbl0701.58023MR1030854
  13. [13] V. Benci and F. Giannoni, Homoclinic orbits on compact manifolds, preprint, Università di Pisa, 1989. Zbl0737.58052MR1112335
  14. [14] V. Coti-Zelati and I. Ekeland, A variational approach to homoclinic orbits in Hamiltonian systems, preprint, S.I.S.S.A., 1988. Zbl0731.34050

Citations in EuDML Documents

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  1. Marek Izydorek, Joanna Janczewska, The shadowing chain lemma for singular Hamiltonian systems involving strong forces
  2. Joanna Janczewska, The Existence and Multiplicity of Heteroclinic and Homoclinic Orbits for a Class of Singular Hamiltonian Systems in 𝐑 2
  3. Joanna Janczewska, Jakub Maksymiuk, Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3
  4. Paolo Caldiroli, Margherita Nolasco, Multiple homoclinic solutions for a class of autonomous singular systems in R2
  5. Fabio Giannoni, Louis Jeanjean, Kazunaga Tanaka, Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems
  6. Antonio Ambrosetti, Critical points and nonlinear variational problems

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