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Bumps of Potentials and Almost Periodic Oscillations

Volume 12, Number 2 (2011), 122 - 133

Bumps of Potentials and Almost Periodic Oscillations

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Abstract

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.