Abstract

Let U ∈ C2(Ω), where Ω is a bounded set in ℝN Suppose that U(x) tends to + ∞ as x tends to ∂Ω. Our main results concern the existence of periodic solutions of \( −x\limits^{¨} + \mathrm{U}′(x) \) having a prescribed number T as minimal period. The results are also generalized to first order Hamiltonian systems.

Résumé

Soit U ∈ C2(Ω), où Ω est un ouvert donné de ℝN. On suppose que U(x) → + ∞ quand x → ∂Ω. On montre l’existence de solutions périodiques de \( x\limits^{¨} + \mathrm{U}′(x) = 0 \), de période minimale prescrite. On étend ces résultats aux systèmes hamiltoniens du premier ordre.