The fixed energy problem for a class of nonconvex singular Hamiltonian systems

C. Carminati, É Séré, K. Tanaka

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We consider a noncompact hypersurface H in R2 N which is the energy level of a singular Hamiltonian of "strong force" type. Under global geometric assumptions on H, we prove that it carries a closed characteristic, as a consequence of a result by Hofer and Viterbo on the Weinstein conjecture in cotangent bundles of compact manifolds. Our theorem contains, as particular cases, earlier results on the fixed energy problem for singular Lagrangian systems of strong force type.

Original languageEnglish
Pages (from-to)362-377
Number of pages16
JournalJournal of Differential Equations
Volume230
Issue number1
DOIs
Publication statusPublished - 2006 Nov 1

Keywords

  • Closed characteristic
  • Cotangent bundle
  • Critical point theory
  • Hamiltonian system
  • Hypersurface of contact type
  • Singular potential
  • Strong force
  • Variational methods
  • Weinstein conjecture

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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