Normal modes of a Lagrangian system constrained in a potential well
- 1 October 1984
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Vol. 1 (5) , 379-400
- https://doi.org/10.1016/s0294-1449(16)30419-x
Abstract
Let a, U \in C^2(Ω) where Ω is a bounded set in ℝ^n and let \mathrm{L}\left(x,\xi \right) = \frac{1}{2}a\left(x\right)\left|\xi \right|^{2}−\mathrm{U}\left(x\right),\:\:x \in Ω;\xi \in ℝ^{n}. We suppose that a, U > 0 for x \in Ω and that \lim \limits_{x\rightarrow ∂Ω}\mathrm{U}\left(x\right) = + ∞. Under some smoothness assumptions, we prove that the Lagrangian system associated with the above Lagrangian \mathrm{L} has infinitely many periodic solutions of any period \mathrm{T} .This publication has 5 references indexed in Scilit:
- Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural Hamiltonian systemsAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 1984
- Applications of Natural Constraints in Critical Point Theory to Boundary Value Problems on Domains with Rotation Symmetry.Published by Defense Technical Information Center (DTIC) ,1983
- Periodic solutions of large norm of Hamiltonian systemsJournal of Differential Equations, 1983
- Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinityNonlinear Analysis, 1983
- The Direct Method in the Study of Periodic Solutions of Hamiltonian Systems with Prescribed PeriodPublished by Springer Nature ,1983