Attractors of retarded first order lattice systems

In this paper, we study the following retarded first order lattice systems (where u it = u i ( t + s ) denotes the delay term, s belongs to the interval of delay time [−ν, 0], and ν > 0 is a constant, see section 3 for details) and obtain the existence of a global attractor for each fixed ν > 0 in C ([−ν, 0]; ℓ 2 ). Then we establish the upper semi-continuity (in a suitable sense) of as ν → 0 + . Finally, we make some remarks.