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

研究成果: Article › 査読

40 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	427-438
ページ数	12
ジャーナル	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
巻	7
号	5
DOI	https://doi.org/10.1016/S0294-1449(16)30285-2
出版ステータス	Published - 1990 9月 1
外部発表	はい

ASJC Scopus subject areas

分析
数理物理学
応用数学

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10.1016/S0294-1449(16)30285-2

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N2 - 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.

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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KW - minimax argument

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Homoclinic orbits for a singular second order Hamiltonian system

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