Bumps of potentials and almost periodic oscillations.
Résumé
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.