Attractors for first order lattice systems with almost periodic nonlinear part

We study the existence of the uniform global attractor for a family of infinite dimensional first order non-autonomous lattice dynamical systems of the following form: {document}$ {equation*} {.}{u}+Au+α u+f( u,t) = g( t) ,\,\,( g,f) ∈ H( ( g₀,f₀) ) ,t>τ ,τ ∈ R, {equation*} document with initial data document {equation*} u( τ ) = uτ. {equation*} document The nonlinear part of the system f( u,t) $ presents the main difficultly of this work. To overcome this difficulty we introduce a suitable Banach space $ W $ of functions satisfying (3)-(7) with norm (8) such that $ f₀( · ,t) $ is an almost periodic function of $ t $ with values in $ W $ and $ ( g,f) ∈ H( ( g₀,f₀) ) $.