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 language | English |
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Pages (from-to) | 427-438 |
Number of pages | 12 |
Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
Volume | 7 |
Issue number | 5 |
DOIs | |
Publication status | Published - 1990 Sept 1 |
Externally published | Yes |
Keywords
- 58 E 05
- 58 F 05
- Homoclinic orbit
- critical point
- minimax argument
- singular potential
ASJC Scopus subject areas
- Analysis
- Mathematical Physics
- Applied Mathematics