Bumps of potentials and almost periodic oscillations.

Joël Blot (1) , Dhaou Lassoued (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

We establish the existence of a Besicovitch almost periodic solution of a second-order differential equation, u''(t) + DV(u(t),t) = 0, in a Hilbert space, when the potential V(.,t) possesses a bump surrounded by a hollow. We use a variational method on a Hiolbert space of Besicovitch almost periodic functions.

Mots clés: almost periodic function; second-order differential equation; variational methods

Domaines: Systèmes dynamiques [math.DS]

Joël Blot, Dhaou Lassoued. Bumps of potentials and almost periodic oscillations.. African Diaspora Journal of Mathematics, 2011, 12 (2), pp.122-133. ⟨hal-00662543⟩