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Bumps of potentials and almost periodic oscillations. (English) Zbl 1244.34081

Summary: We establish the existence of a Besicovitch almost periodic solution of the 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.

MSC:

34G10 Linear differential equations in abstract spaces
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
58E30 Variational principles in infinite-dimensional spaces
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References:

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