### Abstract

We study the existence of unbounded solutions of singular Hamiltonian systems: q̈ + ∇V(q)=0, (*) where V(q) ∼ -1/|q|^{α} is a potential with a singularity. For a class of singular potentials with a strong force α > 2, we show the existence of at least one hyperbolic-like solutions. More precisely, for given H > 0 and θ_{+}, θ_{-} ε S^{N-1}, we find a solution q(t) of (*) satisfying 1/2 |q̇|^{2} + V(q) = H, |q(t) |→ as t → ±∞ lim_{t→±∞} q(t)/|q(t)|=θ±.

Original language | English |
---|---|

Pages (from-to) | 43-65 |

Number of pages | 23 |

Journal | Nonlinear Differential Equations and Applications |

Volume | 7 |

Issue number | 1 |

Publication status | Published - 2000 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Nonlinear Differential Equations and Applications*,

*7*(1), 43-65.

**Hyperbolic-like solutions for singular Hamiltonian systems.** / Felmer, Patricio; Tanaka, Kazunaga.

Research output: Contribution to journal › Article

*Nonlinear Differential Equations and Applications*, vol. 7, no. 1, pp. 43-65.

}

TY - JOUR

T1 - Hyperbolic-like solutions for singular Hamiltonian systems

AU - Felmer, Patricio

AU - Tanaka, Kazunaga

PY - 2000

Y1 - 2000

N2 - We study the existence of unbounded solutions of singular Hamiltonian systems: q̈ + ∇V(q)=0, (*) where V(q) ∼ -1/|q|α is a potential with a singularity. For a class of singular potentials with a strong force α > 2, we show the existence of at least one hyperbolic-like solutions. More precisely, for given H > 0 and θ+, θ- ε SN-1, we find a solution q(t) of (*) satisfying 1/2 |q̇|2 + V(q) = H, |q(t) |→ as t → ±∞ limt→±∞ q(t)/|q(t)|=θ±.

AB - We study the existence of unbounded solutions of singular Hamiltonian systems: q̈ + ∇V(q)=0, (*) where V(q) ∼ -1/|q|α is a potential with a singularity. For a class of singular potentials with a strong force α > 2, we show the existence of at least one hyperbolic-like solutions. More precisely, for given H > 0 and θ+, θ- ε SN-1, we find a solution q(t) of (*) satisfying 1/2 |q̇|2 + V(q) = H, |q(t) |→ as t → ±∞ limt→±∞ q(t)/|q(t)|=θ±.

UR - http://www.scopus.com/inward/record.url?scp=0346986089&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346986089&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 43

EP - 65

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

SN - 1021-9722

IS - 1

ER -