Attractors for second order lattice systems with almost periodic symbols in weighted spaces

We study the existence of a uniform global attractor for a family of second order non-autonomous lattice dynamical systems with almost periodic symbols in a suitable weighted space of infinite sequences. The assumptions on the nonlinear part present the main difficulty of this work. Lemma 2 and Lemma 4 are helpful to overcome such a difficulty. A uniform absorbing set O and uniform estimates on the tails of solutions with respect to initial data from O and all translations of the external term involved are introduced. Such uniform estimates are needed to obtain the asymptotic compactness of solution operators which is a major step towards proving the existence of attractors.