In this paper we consider an equation of type $q''(t)=\partial_2 V(t,q(t))$, where $V$ is quasi-periodic (q.p.) in $t$, uniformly w.r.t. to $q$, is convex w.r.t. $q$ for each $t$. We look for q.p. solutions $q:\R \to \IH$ (where $\IH$ is an Hilbert space) to this equation. By using the formalism introduced by the Physician Percival, it is possible to transform this problem in a elliptic degenerate Partial Differential Equation on the torus. By using a singular perturbation method, we obtain existence results under technical assumptions on $V$.