Homoclinic orbits for a singular second order Hamiltonian system

Research output: Contribution to journalArticle

37 Citations (Scopus)

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 languageEnglish
Pages (from-to)427-438
Number of pages12
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume7
Issue number5
DOIs
Publication statusPublished - 1990 Sep 1
Externally publishedYes

Fingerprint

Second Order Hamiltonian System
Hamiltonians
Homoclinic Orbit
Orbits
Uniqueness
Singularity

Keywords

  • 58 E 05
  • 58 F 05
  • critical point
  • Homoclinic orbit
  • minimax argument
  • singular potential

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

Cite this

Homoclinic orbits for a singular second order Hamiltonian system. / Tanaka, Kazunaga.

In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 7, No. 5, 01.09.1990, p. 427-438.

Research output: Contribution to journalArticle

@article{134a27619bd240d887674f00f3e1af41,
title = "Homoclinic orbits for a singular second order Hamiltonian system",
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.",
keywords = "58 E 05, 58 F 05, critical point, Homoclinic orbit, minimax argument, singular potential",
author = "Kazunaga Tanaka",
year = "1990",
month = "9",
day = "1",
doi = "10.1016/S0294-1449(16)30285-2",
language = "English",
volume = "7",
pages = "427--438",
journal = "Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis",
issn = "0294-1449",
publisher = "Elsevier Masson SAS",
number = "5",

}

TY - JOUR

T1 - Homoclinic orbits for a singular second order Hamiltonian system

AU - Tanaka, Kazunaga

PY - 1990/9/1

Y1 - 1990/9/1

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 - critical point

KW - Homoclinic orbit

KW - minimax argument

KW - singular potential

UR - http://www.scopus.com/inward/record.url?scp=0001260280&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001260280&partnerID=8YFLogxK

U2 - 10.1016/S0294-1449(16)30285-2

DO - 10.1016/S0294-1449(16)30285-2

M3 - Article

VL - 7

SP - 427

EP - 438

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 -