Multiple periodic solutions for Hamiltonian systems with singular potential

Addolorata Salvatore

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1992)

  • Volume: 3, Issue: 2, page 111-119
  • ISSN: 1120-6330

Abstract

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In this Note we prove the existence of infinitely many periodic solutions of prescribed period for a Hamiltonian system with a singular potential.

How to cite

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Salvatore, Addolorata. "Multiple periodic solutions for Hamiltonian systems with singular potential." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 3.2 (1992): 111-119. <http://eudml.org/doc/244227>.

@article{Salvatore1992,
abstract = {In this Note we prove the existence of infinitely many periodic solutions of prescribed period for a Hamiltonian system with a singular potential.},
author = {Salvatore, Addolorata},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Singular Hamiltonian systems; Periodic solutions; Critical points; Hamiltonian system; infinitely many periodic solutions of prescribed period},
language = {eng},
month = {6},
number = {2},
pages = {111-119},
publisher = {Accademia Nazionale dei Lincei},
title = {Multiple periodic solutions for Hamiltonian systems with singular potential},
url = {http://eudml.org/doc/244227},
volume = {3},
year = {1992},
}

TY - JOUR
AU - Salvatore, Addolorata
TI - Multiple periodic solutions for Hamiltonian systems with singular potential
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1992/6//
PB - Accademia Nazionale dei Lincei
VL - 3
IS - 2
SP - 111
EP - 119
AB - In this Note we prove the existence of infinitely many periodic solutions of prescribed period for a Hamiltonian system with a singular potential.
LA - eng
KW - Singular Hamiltonian systems; Periodic solutions; Critical points; Hamiltonian system; infinitely many periodic solutions of prescribed period
UR - http://eudml.org/doc/244227
ER -

References

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  1. AMBROSETTI, A. - COTI ZELATI, V., Critical points with lack of compactness and singular dynamical systems. Ann. Mat. Pura e Appl., 149, 1987, 237-259. Zbl0642.58017MR932787DOI10.1007/BF01773936
  2. AMBROSETTI, A. - COTI ZELATI, V., Non collision orbits for a class of Keplerian-like potentials. Ann. Inst. H. Poincaré, 5, 1988, 287-295. Zbl0667.58055MR954474
  3. BAHRI, B. - RABINOWITZ, P. H., A minimax method for a class of Hamiltonian systems with singular potentials. J. Funct. Anal., 82, 1989, 412-428. Zbl0681.70018MR987301DOI10.1016/0022-1236(89)90078-5
  4. BENCI, V., A new approach to the Morse-Conley theory. In: G. F. DELL' ANTONIO - B. D'ONOFRIO (eds.), Proceedings on Recent advances in Hamiltonian systems. World Scientific, Singapore1987, 83-96. Zbl0663.70028MR902622
  5. BENCI, V. - GIANNONI, F., Closed geodesics on non compact Riemannian manifolds. Compt. Rend. Acad. Sc. Paris, 312, I, 1991, 857-861. Zbl0739.53038MR1108507
  6. BENCI, V. - GIANNONI, F., On the closed geodesics on non compact Riemannian manifolds. Preprint. 
  7. CAPOZZI, A. - FORTUNATO, D. - SALVATORE, A., Periodic solutions of Lagrangian systems with bounded potential. J. Math. Anal. Appl., 124, 1987, 482-494. Zbl0664.34053MR887004DOI10.1016/0022-247X(87)90009-6
  8. CAPOZZI, A. - GRECO, C. - SALVATORE, A., Lagrangian systems in the presence of singularities. Proc. Amer. Math. Soc., 102, 1988, 125-130. Zbl0664.34054MR915729DOI10.2307/2046044
  9. DE GIOVANNI, M. - GIANNONI, F., Periodic solutions of dynamical systems with Newtonian type potentials. Ann. Scuola Norm. Sup. Pisa, 15, 1988, 467-494. Zbl0692.34050
  10. DE GIOVANNI, M. - GIANNONI, F. - MARINO, A., Dynamical systems with Newtonian type potentials. Atti Acc. Lincei Rend. fis., s. 8, 81, 1987, 271-278. Zbl0667.70010MR999819
  11. GIANNONI, F., Geodesics on non static Lorentz manifolds of Reissner-Nordstrôm type. Math. Annalen., 291, 1991, 383-401. Zbl0725.53048MR1133338DOI10.1007/BF01445215
  12. GORDON, W. B., Conservative dynamical systems involving strong forces. Trans. Amer. Mat. Soc.204, 1975, 113-135. Zbl0276.58005MR377983
  13. GRECO, C., Periodic solutions of a class of singular Hamiltonian systems. Nonlinear Anal. T.M.A., 12, 1988, 259-270. Zbl0648.34048MR928560DOI10.1016/0362-546X(88)90112-5
  14. MAJER, P., Ljusternik-Schnirelman theory with local Palais-Smale condition and singular dynamical systems. Ann. Inst. H. Poincaré, 8, 5, 1991, 459-476. Zbl0749.58046MR1136352
  15. VITERBO, C., Indice de Morse des points critiques obtenus par minimax. 1988, Ann. Inst. H. Poincaré, 5, 1988, 221-225. Zbl0695.58007MR954472

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