A remark on periodic solutions of singular Hamiltonian systems

Original Paper

DOI: 10.1007/s00030-003-1069-y

Cite this article as:
Adachi, S., Tanaka, K. & Terui, M. Nonlinear differ. equ. appl. (2005) 12: 265. doi:10.1007/s00030-003-1069-y


In this note we study the existence of non-collision periodic solutions for singular Hamiltonian systems with weak force. In particular for potential \(V(t,q) \sim - \frac{1}{{{\text{dist}}(q,D)^{\alpha} }},\) where D is a compact C3-surface in \(\mathbb{R}^{N} ,\) we prove the existence of a non-collision periodic solution.

Mathematics Subject Classification (2000).

58F22 34C25 

Key words.

Singular Hamiltonian system periodic solution 

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • Shinji Adachi
    • 1
    • 2
  • Kazunaga Tanaka
    • 1
  • Masahito Terui
    • 1
  1. 1.Department of Mathematics School of Science and EngineeringWaseda UniversityTokyoJapan
  2. 2.Division of Applied Science and Basic Engineering, Faculty of EngineeringShizuoka UniversityShizuokaJapan

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