Genericity of the multibump dynamics for almost periodic Duffing-like systems

In this paper we consider 'slowly' oscillating perturbations of almost peri odic Duffing-like systems, i.e. systems of the form (u) double over dot = u - (a(t) + alpha(omega t))W'(u), t is an element of R, u is an element of R -N, where W is an element of C-2N(R-N, R) is superquadratic and a and alpha are positive and almost periodic. By variational methods, we prove that if omega > 0 is small enough, then the system admits a multibump dynamics. As a consequence we get that the system (u) double over dot = u - a(t)W'(u), t is an element of R, u is an element of R-N, admits multibump solutions wh enever a belongs to an open dense subset of the set of positive almost peri odic continuous functions.