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 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 | |
| Publication status | Published - 1990 Sep 1 |
| Externally published | Yes |
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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 journal › Article
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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 -