In order to show the existence of a.p. (almost Periodic solutions of a Euler-Lagrange equation with a convex lagrangian and an a.p. forcing term, we introduce an hilbertian space (like a Sobolev space) of Besicovitch-a.p. functions and a notion of weak a.p. solution. We use the calculus of variations in mean and the Minty-monotonic operators.