Homoclinic orbits for a singular second order Hamiltonian system

Kazunaga Tanaka

doi:10.1016/S0294-1449(16)30285-2

Homoclinic orbits for a singular second order Hamiltonian system

Kazunaga Tanaka

Research output: Contribution to journal › Article

39 Citations (Scopus)

Abstract

We consider the second order Hamiltonian system: q.+V′(q)=0 where q = (q₁, …, q_N) ∈ R^N(N ≧ 3) and V:R^N\{e} → R(e ∈ R^N) 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
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	https://doi.org/10.1016/S0294-1449(16)30285-2
Publication status	Published - 1990 Sep 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

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10.1016/S0294-1449(16)30285-2

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Tanaka, K. (1990). Homoclinic orbits for a singular second order Hamiltonian system. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 7(5), 427-438. https://doi.org/10.1016/S0294-1449(16)30285-2

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AB - 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.

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