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Hyperbolic-like solutions for singular Hamiltonian systems

  • Patricio Felmer
  • Kazunaga Tanaka

Abstract.

We study the existence of unbounded solutions of singular Hamiltonian systems: \(\ddot q + \nabla V(q) = 0,\) where \(V(q) \sim -{1\over{|q|^\alpha}}\) is a potential with a singularity. For a class of singular potentials with a strong force \(\alpha>2\), we show the existence of at least one hyperbolic-like solutions. More precisely, for given \(H>0\) and \(\theta_+, \theta_-\in S^{N-1}\), we find a solution q(t) of (*) satisfying \({1\over 2} |\dot q|^2 + V(q) = H,\) \(|q(t)| \longrightarrow \infty \quad {as} \quad t\longrightarrow\pm\infty\) \(\lim \limits_{t\to\pm\infty} {q(t)\over |q(t)|} = \theta_\pm.\)

Keywords

Hamiltonian System Strong Force Singular Potential Unbounded Solution Singular Hamiltonian System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel, 2000

Authors and Affiliations

  • Patricio Felmer
    • 1
  • Kazunaga Tanaka
    • 2
  1. 1.Departamento de Ingeniería Matemática F.C.F.M., Universidad de Chile, Casilla 170 Correo 3, Santiago, ChileCH
  2. 2.Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169, Japan, e-mail: kazunaga@mn.waseda.ac.jpJP

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