Calculus of Variations and Partial Differential Equations

, Volume 5, Issue 6, pp 523–555

Multiplicity of homoclinics for a class of time recurrent second order Hamiltonian systems

  • Piero Montecchiari
  • Margherita Nolasco
  • Susanna Terracini

DOI: 10.1007/s005260050078

Cite this article as:
Montecchiari, P., Nolasco, M. & Terracini, S. Calc Var (1997) 5: 523. doi:10.1007/s005260050078

Abstract.

We prove the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems in \({\Bbb R}^N\) of the form \(\ddot q=q-W'(t,q)\), where we assume the existence of a sequence \((t_n)\subset{\Bbb R}\) such that \(t_n\to \pm\infty\) and \(W'(t+t_n,x)\to W'(t,x)\) as \(n\to\pm\infty\) for any \((t,x)\in{\Bbb R}\times{\Bbb R}^N\). Moreover, under a suitable non degeneracy condition, we prove that this class of systems admits multibump solutions.

Mathematics Subject Classification (1991): 58E05; 34C37; 58F15; 70H05

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Piero Montecchiari
    • 1
  • Margherita Nolasco
    • 2
  • Susanna Terracini
    • 3
  1. 1. Universitá degli studi di Trieste, Dipartimento di Matematica, Piazzale Europa 1, I-34013 Trieste, Italy; e-mail: montec@univ.trieste.it IT
  2. 2. Scuola Internazionale Superiore di Studi Avanzati, via Beirut 4, I-34013 Trieste, Italy; e–mail: nolasco@neumann.sissa.it IT
  3. 3. Dipartimento di Matematica del Politecnico, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy; e–mail: suster@ipmmA1.mate.polimi.it IT