Homoclinic orbits for a singular second order Hamiltonian system

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Abstract

We consider the second order Hamiltonian system: q.+V′(q)=0 where q = (q1, …, qN) ∈ RN(N ≧ 3) and V:RN\{e} → R(e ∈ RN) is a potential with a singularity, i.e., |V(q)| → ∞ as q →e. We prove the existence of a homoclinic orbit of (HS) under suitable assumptions. Our main assumptions are the strong force condition of Gordon [8] and the uniqueness of a global maximum of V.

Original languageEnglish
Pages (from-to)427-438
Number of pages12
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume7
Issue number5
DOIs
Publication statusPublished - 1990 Sep 1
Externally publishedYes

Keywords

  • 58 E 05
  • 58 F 05
  • Homoclinic orbit
  • critical point
  • minimax argument
  • singular potential

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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