Abstract
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 language | English |
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Pages (from-to) | 211-220 |
Number of pages | 10 |
Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
Volume | 5 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 May 1988 |
Keywords
- 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