### 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 |
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Pages (from-to) | 43-65 |

Number of pages | 23 |

Journal | Nonlinear Differential Equations and Applications |

Volume | 7 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2000 Jan 1 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics