Periodic solutions of hamiltonian systems of 3-body type

A. Bahri; P. H. Rabinowitz

Annales de l'I.H.P. Analyse non linéaire (1991)

  • Volume: 8, Issue: 6, page 561-649
  • ISSN: 0294-1449

How to cite

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Bahri, A., and Rabinowitz, P. H.. "Periodic solutions of hamiltonian systems of 3-body type." Annales de l'I.H.P. Analyse non linéaire 8.6 (1991): 561-649. <http://eudml.org/doc/78265>.

@article{Bahri1991,
author = {Bahri, A., Rabinowitz, P. H.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {periodic solutions; Hamiltonian systems; functional; critical points},
language = {eng},
number = {6},
pages = {561-649},
publisher = {Gauthier-Villars},
title = {Periodic solutions of hamiltonian systems of 3-body type},
url = {http://eudml.org/doc/78265},
volume = {8},
year = {1991},
}

TY - JOUR
AU - Bahri, A.
AU - Rabinowitz, P. H.
TI - Periodic solutions of hamiltonian systems of 3-body type
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1991
PB - Gauthier-Villars
VL - 8
IS - 6
SP - 561
EP - 649
LA - eng
KW - periodic solutions; Hamiltonian systems; functional; critical points
UR - http://eudml.org/doc/78265
ER -

References

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  2. [2] A. Bahri and P.H. Rabinowitz, A Minimax Method for a Class of Hamiltonian Systems with Singular Potentials, J. Functional Anal., Vol. 82, 1989, pp. 412-428. Zbl0681.70018MR987301
  3. [3] A. Ambrosetti and V. Coti-Zelati, Critical Points with Lack of Compactness and Applications to Singular Hamiltonian Systems (to appear). Zbl0642.58017MR1281984
  4. [4] M. Degiovanni, F. Giannoni and A. Marino, Periodic Solutions of Dynamical Systems with Newtonian Type Potentials, in Periodic Solutions of Hamiltonian Systems and Related Topics, P. H. RABINOWITZ et al., Vol. 29, pp. 111-115, NATO ASI Series, Reidel, Dordrecht, 1987. Zbl0632.34038MR920613
  5. [5] W.B. Gordon, Conservative Dynamical Systems Involving Strong Forces, Trans. Am. Math. Soc., Vol. 204, 1975, pp. 113-135. Zbl0276.58005MR377983
  6. [6] C. Greco, Periodic Solutions of a Class of Singular Hamiltonian Systems, Nonlinear Analysis: TMA, Vol. 12, 1988, pp. 259-270. Zbl0648.34048MR928560
  7. [7] A. Marino and G. Prodi, Metodi perturbativi nella teoria di Morse, Boll. Un. Mat. Ital., Vol. 11, 1975, pp. 1-32. Zbl0311.58006MR418150
  8. [8] A. Bahri, Thèse de Doctorat d'État, Univ. P. and M. Curie, Paris, 1981. 
  9. [9] A. Bahri and H. Berestycki, Forced vibrations of superquadratic Hamiltonian systems, Acta Math, Vol. 152, 1984, pp. 143-197. Zbl0592.70027MR741053
  10. [10] Borsuk, Shape Theory, Zbl0317.55006
  11. [11] D. Sullivan and M. Vigué-Poirier, The Homology Theory of the Closed Geodesic Problem, J. Diff. Geom., Vol. 11, 1976, pp. 633-644. Zbl0361.53058MR455028
  12. [12] A. Dold, Lectures on Algebraic Topology, Springer-Verlag, Heidelberg, 1972. Zbl0234.55001MR415602
  13. [13] P.H. Rabinowitz, Periodic Solutions for Some Forced Singular Hamiltonian Systems, (to appear), Festschift in honor of Jürgen Moser. Zbl0790.70019MR1039360
  14. [14] C.C. Conley, Isolated Invariant Sets and the Morse Index, C.B.M.S. Regional Conference Series in Math, # 38, Am. Math. Soc., Providence R. I., 1978. Zbl0397.34056MR511133
  15. [15] A. Bahri, (to appear). 
  16. [16] M.W. Hirsch, Differential Topology, Springer-Verlag, 1976. Zbl0356.57001MR448362
  17. [17] E. Spanier, Algebraic Topology, McGraw-Hill, 1966. Zbl0145.43303MR210112
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  19. [19] I. Ekeland, Une théorie de Morse pour les systèmes Hamiltoniens convexes, Ann. Inst. H. Poincaré: Analyse non linéaire, Vol. 1, 1984, pp. 19-78. Zbl0537.58018MR738494
  20. [20] A. Bahri and B.M. D'Oonofrio, (to appear). 

Citations in EuDML Documents

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  1. A. Bahri, P. H. Rabinowitz, Periodic solutions of some problems of 3-body type
  2. E. Fadell, S. Husseini, Infinite cup length in free loop spaces with an application to a problem of the N-body type
  3. Antonio Ambrosetti, Kazunaga Tanaka, Enzo Vitillaro, Periodic solutions with prescribed energy for some keplerian N -body problems
  4. Dina Abuzaid, Randa Ben Mahmoud, Hichem Chtioui, Afef Rigane, Topological tools for the prescribed scalar curvature problem on S n
  5. Mohamed Ben Ayed, Mohameden Ould Ahmedou, Multiplicity results for the prescribed scalar curvature on low spheres
  6. Vivina Barutello, Simone Secchi, Morse index properties of colliding solutions to the N-body problem
  7. Randa Ben Mahmoud, Hichem Chtioui, Existence results for the prescribed Scalar curvature on S 3
  8. Khalil El Mehdi, Prescribing Q -curvature on higher dimensional spheres
  9. Claude Viterbo, Orbites périodiques dans le problème des trois corps
  10. Pengfei Yuan, Shiqing Zhang, New Periodic Solutions for N-Body Problems with Weak Force Potentials

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