Dynamical systems with Newtonian type potentials

Marco Degiovanni; Fabio Giannoni; Antonio Marino

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1987)

  • Volume: 81, Issue: 3, page 271-277
  • ISSN: 1120-6330

Abstract

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We study the existence of regular periodic solutions to some dynamical systems whose potential energy is negative, has only a singular point and goes to zero at iniìnity. We give sufficient conditions to the existence of periodic solutions of assigned period which do not meet the singularity.

How to cite

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Degiovanni, Marco, Giannoni, Fabio, and Marino, Antonio. "Dynamical systems with Newtonian type potentials." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 81.3 (1987): 271-277. <http://eudml.org/doc/287460>.

@article{Degiovanni1987,
abstract = {We study the existence of regular periodic solutions to some dynamical systems whose potential energy is negative, has only a singular point and goes to zero at iniìnity. We give sufficient conditions to the existence of periodic solutions of assigned period which do not meet the singularity.},
author = {Degiovanni, Marco, Giannoni, Fabio, Marino, Antonio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Dynamical systems; Newtonian potential; Periodic solutions; existence of regular periodic solutions; dynamical systems; existence of periodic solutions},
language = {eng},
month = {9},
number = {3},
pages = {271-277},
publisher = {Accademia Nazionale dei Lincei},
title = {Dynamical systems with Newtonian type potentials},
url = {http://eudml.org/doc/287460},
volume = {81},
year = {1987},
}

TY - JOUR
AU - Degiovanni, Marco
AU - Giannoni, Fabio
AU - Marino, Antonio
TI - Dynamical systems with Newtonian type potentials
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1987/9//
PB - Accademia Nazionale dei Lincei
VL - 81
IS - 3
SP - 271
EP - 277
AB - We study the existence of regular periodic solutions to some dynamical systems whose potential energy is negative, has only a singular point and goes to zero at iniìnity. We give sufficient conditions to the existence of periodic solutions of assigned period which do not meet the singularity.
LA - eng
KW - Dynamical systems; Newtonian potential; Periodic solutions; existence of regular periodic solutions; dynamical systems; existence of periodic solutions
UR - http://eudml.org/doc/287460
ER -

References

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  1. AMBROSETTI, A. and COTI ZELATI, V. - Solutions with minimal period for Hamiltonian systems in a potential well, «Ann. Inst. H. Poincaré. Anal. Non Linéaire», in press. Zbl0623.58013
  2. AMBROSETTI, A. and COTI ZELATI, V. - Critical points with lack of compactness and singular dynamical systems, «Ann. Mat. Pura Appl.», in press. Zbl0642.58017
  3. BENCI, V. (1984) - Normal modes of a Lagrangian system constrained in a potential well, «Ann. Inst. H. Poincaré. Anal. Non Linéaire », 1, 379-400. Zbl0561.58006MR779875
  4. CAPOZZI, A., GRECO, C. and SALVATORE, A. (1985) - Lagrangian systems in presence of singularities, preprint, Dip. Mat., Bari. Zbl0664.34054MR915729DOI10.2307/2046044
  5. COTI ZELATI, V. - Dynamical systems with effective-like potentials, «Nonlinear Anal.», in press. Zbl0648.34050MR926213DOI10.1016/0362-546X(88)90035-1
  6. GORDON, W.B. (1975) - Conservative dynamical systems involving strong forces, «Trans. Amer. Math. Soc.», 204, 113-135. Zbl0276.58005MR377983
  7. GORDON, W.B. (1977) - A minimizing property of Keplerian orbits, «Amer. J. Math.», 99, 961-971. Zbl0378.58006MR502484
  8. GRECO, C. (1985) - Periodic solutions of some nonlinear ODE with singular nonlinear part, preprint, Dip. Mat., Bari. Zbl0644.34034MR916285
  9. GRECO, C. (1986) - Periodic solutions of a class of singular Hamiltonian systems, Dip. Mat., Bari. Zbl0648.34048
  10. RABINOWITZ, P.H. (1982) - Periodic solutions of Hamiltonian systems: a survey, «SIAM J. Math. Anal.», 13, 343-352. Zbl0521.58028MR653462DOI10.1137/0513027

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