Multiplicity of homoclinic orbits for a class of asymptotically periodic Hamiltonian systems

Piero Montecchiari

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 4, page 265-271
  • ISSN: 1120-6330

Abstract

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We prove the existence of infinitely many geometrically distinct homoclinic orbits for a class of asymptotically periodic second order Hamiltonian systems.

How to cite

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Montecchiari, Piero. "Multiplicity of homoclinic orbits for a class of asymptotically periodic Hamiltonian systems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.4 (1993): 265-271. <http://eudml.org/doc/244177>.

@article{Montecchiari1993,
abstract = {We prove the existence of infinitely many geometrically distinct homoclinic orbits for a class of asymptotically periodic second order Hamiltonian systems.},
author = {Montecchiari, Piero},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Hamiltonian systems; Homoclinic orbits; Multibump solutions; Minimax argument; asymptotically periodic Hamiltonian system; infinitely many homoclinic solutions; -bump solutions},
language = {eng},
month = {12},
number = {4},
pages = {265-271},
publisher = {Accademia Nazionale dei Lincei},
title = {Multiplicity of homoclinic orbits for a class of asymptotically periodic Hamiltonian systems},
url = {http://eudml.org/doc/244177},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Montecchiari, Piero
TI - Multiplicity of homoclinic orbits for a class of asymptotically periodic Hamiltonian systems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/12//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 4
SP - 265
EP - 271
AB - We prove the existence of infinitely many geometrically distinct homoclinic orbits for a class of asymptotically periodic second order Hamiltonian systems.
LA - eng
KW - Hamiltonian systems; Homoclinic orbits; Multibump solutions; Minimax argument; asymptotically periodic Hamiltonian system; infinitely many homoclinic solutions; -bump solutions
UR - http://eudml.org/doc/244177
ER -

References

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  1. ALAMA, S. - LI, Y. Y., On «Multibump» Bound States for Certain Semilinear Elliptic Equations. Research Report No. 92-NA-012. Carnegie Mellon University, 1992. Zbl0796.35043MR1206338DOI10.1512/iumj.1992.41.41052
  2. AMBROSETTI, A., Critical points and nonlinear variational problems. Bul. Soc. Math. France, 120, 1992. Zbl0766.49006MR1164129
  3. COTI ZELATI, V. - EKELAND, I. - SÉRÉ, E., A Variational approach to homoclinic orbits in Hamiltonian systems. Math. Ann., 288, 1990, 133-160. Zbl0731.34050MR1070929DOI10.1007/BF01444526
  4. COTI ZELATI, V. - RABINOWITZ, P. H., Homoclinic orbits for second order hamiltonian systems possessing superquadratic potentials. J. Amer. Math. Soc., 4, 1991, 693-727. Zbl0744.34045MR1119200DOI10.2307/2939286
  5. HOFER, H. - WISOCKI, K., First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems. Math. Ann., 288, 1990, 483-503. Zbl0702.34039MR1079873DOI10.1007/BF01444543
  6. LIONS, P.L., The concentration-compactness principle in the calculus of variations. Rev. Math. Iberoam., 1, 1985, 145-201. Zbl0704.49005MR834360DOI10.4171/RMI/6
  7. MONTECCHIARI, P., Existence and multiplicity of homoclinic orbits for a class of asymptotically periodic second order Hamiltonian systems. Preprint S.I.S.S.A., 1993. Zbl0849.34035MR1378249DOI10.1007/BF01759265
  8. RABINOWITZ, P. H., Homoclinic orbits for a class of Hamiltonian systems. Proc. Roy. Soc. Edinburgh, 1144, 1990, 33-38. Zbl0705.34054MR1051605DOI10.1017/S0308210500024240
  9. SÉRÉ, E., Existence of infinitely many homoclinic orbits in Hamiltonian systems. Math. Z., 209, 1992, 27-42. Zbl0725.58017MR1143210DOI10.1007/BF02570817
  10. SÉRÉ, E., Looking for the Bernoulli shift. Preprint CEREMADE, 1992. Zbl0803.58013MR1249107

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