We establish the existence of a Besicovitch almost periodic solution of a second-order differential equation, $u''(t)+ D_1V(u(t),t) = 0$, in a Hilbert space, when the potential $V(.,t)$ possesses a bump surrounded with a hollow. We use a variational method on a Hilbert space of Besicovitch almost periodic functions.
"Bumps of Potentials and Almost Periodic Oscillations." Afr. Diaspora J. Math. (N.S.) 12 (2) 122 - 133, 2011.