Asymptotic Behavior of a Nonautonomous p-Laplacian Lattice System

The existence of a pullback attractor for the nonautonomous p-Laplacian type equations on infinite lattices is established under certain natural dissipative conditions. In particular, there is no restriction on the power index q of the nonlinearity relative to the index p. The forward limiting behavior is also discussed and, under suitable assumptions on the time dependent terms, the lattice system is shown to be asymptotically autonomous with its pullback attractor component sets converging upper semi-continuously to the autonomous global attractor of the limiting autonomous system.