Existence of nonminal quasiperiodic solutions for second order equations

Abstract

We consider the motion of $n$ particles under the action of a potential $F$. Imposing appropriate conditions on $F$ we obtain quasiperiodic solutions using variational methods. A Diophantine condition on the frequency similar to those encountered in KAM theory allows us to establish the necessary properties of the corresponding functional. The solutions are then obtained by means of the mountain pass theorem on a suitable convex subset.