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 › peer-review

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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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.",

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AU - Tanaka, Kazunaga

PY - 1990/9/1

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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.

KW - 58 E 05

KW - 58 F 05

KW - Homoclinic orbit

KW - critical point

KW - minimax argument

KW - singular potential

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JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

SN - 0294-1449

IS - 5

ER -

Homoclinic orbits for a singular second order Hamiltonian system

Abstract

Keywords

ASJC Scopus subject areas

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