Hyperbolic-like solutions for singular Hamiltonian systems

Patricio Felmer, Kazunaga Tanaka

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 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±.

Original languageEnglish
Pages (from-to)43-65
Number of pages23
JournalNonlinear Differential Equations and Applications
Volume7
Issue number1
DOIs
Publication statusPublished - 2000 Jan 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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