Homoclinic orbits for a singular second order Hamiltonian system
Kazunaga Tanaka
Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya 464, Japan

Abstract
We consider the second order Hamiltonian system:
\[ q\limits^{..} + \mathrm{V}′(q) = 0 \]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.
Résumé
On considère le système hamiltonien du second ordre
\[ q\limits^{..} + \mathrm{V}′(q) = 0 \]où q = (q1, …, qN) ∈ RN(N ≧ 3) et V:RN\{e} → R est un potentiel singulier : |V(q)| → ∞ quand q → e. On montre alors l’existence d’une orbite homocline, sous l’hypothèse dite de « strong farce » (Gordon [8]) et à condition que le maximum de V soit unique.
Cite this article
Kazunaga Tanaka, Homoclinic orbits for a singular second order Hamiltonian system. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), no. 5, pp. 427–438
DOI 10.1016/S0294-1449(16)30285-2