Periodic solutions for a class of Lorenz-Lagrangian systems

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The class of Lorenz-Lagrangian systems under consideration are those of the form −Aq¨=∇V(q), q ∊ ℝn, where A is a real, symmetric matrix with eigenvalues µ1 < 0 < µ2 ≦ … ≦ µn, the corresponding eigenvectors being ei, 1 ≦ i ≦ n. If M+ and M are disjoint infinite submanifolds of ℝn which are the graphs of bounded real-valued functions on span {e2, …, en} with V = 0 on M+ ∪ M, V > 0 on the region Ω between M+ and M, and 〈∇V,e1〉≠0onℝn\Ω, then we show that there exists a periodic solution of this system, provided that ∇V points towards the e1 axis outside a large cylinder centred on the e1 axis.

Original languageEnglish
Pages (from-to)211-220
Number of pages10
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Issue number3
Publication statusPublished - 1 May 1988


  • 34 C 15
  • 34 C 25
  • 34 C 28
  • 34 C 35
  • indefinite Hamilton system
  • Lorenz-Lagrangian system
  • Periodic solution

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics


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