Solutions with minimal period for Hamiltonian systems in a potential well
- 1 June 1987
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Vol. 4 (3) , 275-296
- https://doi.org/10.1016/s0294-1449(16)30369-9
Abstract
Let \mathrm U \in C^2(Ω) , where Ω is a bounded set in ℝ^N . Suppose that \mathrm U(x) tends to + ∞ as x tends to ∂Ω . Our main results concern the existence of periodic solutions of −\"x = \mathrm{U}'(x) having a prescribed number \mathrm T as minimal period. The results are also generalized to first order Hamiltonian systems. Résumé: Soit \mathrm U \in C^2(Ω) , où Ω est un ouvert donné de ℝ^N . On suppose que \mathrm U(x) → + ∞ quand x → ∂Ω . On montre l’existence de solutions périodiques de \"x + \mathrm{U}'(x) = 0 , de période minimale prescrite. On étend ces résultats aux systèmes hamiltoniens du premier ordre.This publication has 10 references indexed in Scilit:
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