Existence and structure results on almost periodic solutions of differenceequations

We study the almost periodic solutions of Euler equations and of some more general Difference Equations. We consider two different notions of almost p eriodic sequences, and we establish some relations between them. We build s uitable sequences spaces and we prove some properties of these spaces. We a lso prove properties of Nemytskii operators on these spaces. We build a var iational approach to establish existence of almost periodic solutions as cr itical points. We obtain existence theorems for nonautonomous linear equati ons and for an Euler equation with a concave and coercive Lagrangian. We al so use a Fixed Point approach to obtain existence results for quasi-linear Difference Equations.