Some properties of collision and non-collision orbits for a class of singular dynamical systems

Vittorio Coti Zelati; Enrico Serra

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

  • Volume: 3, Issue: 3, page 217-222
  • ISSN: 1120-6330

Abstract

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We present some regularity properties of periodic solutions to a class of singular potential problems and we discuss the existence of a regular solution.

How to cite

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Coti Zelati, Vittorio, and Serra, Enrico. "Some properties of collision and non-collision orbits for a class of singular dynamical systems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 3.3 (1992): 217-222. <http://eudml.org/doc/244146>.

@article{CotiZelati1992,
abstract = {We present some regularity properties of periodic solutions to a class of singular potential problems and we discuss the existence of a regular solution.},
author = {Coti Zelati, Vittorio, Serra, Enrico},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Periodic solutions; Kepler problem; Variational methods; variational methods; noncollision solution; regularity properties; periodic solutions; second order Hamiltonian system},
language = {eng},
month = {9},
number = {3},
pages = {217-222},
publisher = {Accademia Nazionale dei Lincei},
title = {Some properties of collision and non-collision orbits for a class of singular dynamical systems},
url = {http://eudml.org/doc/244146},
volume = {3},
year = {1992},
}

TY - JOUR
AU - Coti Zelati, Vittorio
AU - Serra, Enrico
TI - Some properties of collision and non-collision orbits for a class of singular dynamical systems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1992/9//
PB - Accademia Nazionale dei Lincei
VL - 3
IS - 3
SP - 217
EP - 222
AB - We present some regularity properties of periodic solutions to a class of singular potential problems and we discuss the existence of a regular solution.
LA - eng
KW - Periodic solutions; Kepler problem; Variational methods; variational methods; noncollision solution; regularity properties; periodic solutions; second order Hamiltonian system
UR - http://eudml.org/doc/244146
ER -

References

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  1. AMBROSETTI, A. - COTI ZELATI, V., Perturbations of Hamiltonian systems with Keplerian potentials. Math. Z., 201, 1989, 227-242. Zbl0653.34032MR997224DOI10.1007/BF01160679
  2. BAHRI, A. - LIONS, P. L., Morse index of some min-max critical points. I. Application to multiplicity results. Comm. Pure Appl. Math., 41, 1988, 1027-1037. Zbl0645.58013MR968487DOI10.1002/cpa.3160410803
  3. BAHRI, A. - 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. COTI ZELATI, V., Periodic solutions for a class of planar, singular dynamical systems. J. Math. Pures Appl., (9) 68, 1989, 109-119. Zbl0633.34034MR985956
  5. COTI ZELATI, V. - SERRA, E., Collision and non collision solutions for a class of Keplerian like dynamical Systems. Preprint SISSA (Trieste), 1991. Zbl0832.70009MR1313812DOI10.1007/BF01765642
  6. DEGIOVANNI, M. - GIANNONI, F., Periodic solutions of dynamical systems with Newtonian-type potentials. Ann. Scuola Norm. Sup. Pisa Cl. Sci., 4, 1989, 467-494. Zbl0692.34050MR1015804
  7. SERRA, E. - TERRACINI, S., Noncollision solutions to some singular minimization problems with Keplerian-like potentials. Nonlinear Anal. TMA, to appear. Zbl0813.70006MR1256169DOI10.1016/0362-546X(94)90004-3
  8. SOLIMINI, S., Morse index estimates in min-max theorems. Manuscripta Math., 63, 1989, 421-453. Zbl0685.58010MR991264DOI10.1007/BF01171757
  9. TANAKA, K., Morse index at critical points related to the symmetric mountain pass theorem and applications. Commun. in Partial Diff. Eq., 14, 1989, 119-128. Zbl0669.34035MR973271DOI10.1080/03605308908820592
  10. TANAKA, K., Non-collisions for a second order singular Hamiltonian system with weak force. Preprint, Nagoya University, Japan, 1991. MR1220034
  11. TERRACINI, S., An homotopical index and multeplicity of periodic solutions to dynamical systems with singular potentials. J. Diff. Eq., to appear. Zbl0774.34028MR1170468DOI10.1016/0022-0396(92)90090-A
  12. VITERBO, C., Indice de Morse des points critiques obtenus par minimax. Ann. Inst. H. Poincaré, Analyse non linéaire, 3, 1988, 221-225. Zbl0695.58007MR954472

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