Sufficient Criteria for Existence of Pullback Attractors for Stochastic Lattice Dynamical Systems with Deterministic Non-autonomous Terms

摘要

We consider the pullback attractors for non-autonomous dynamical systemsgenerated by stochastic lattice differential equations with non-autonomousdeterministic terms. We first establish a sufficient condition for existence ofpullback attractors of lattice dynamical systems with both non-autonomousdeterministic and random forcing terms. As an application of the abstracttheory, we prove the existence of a unique pullback attractor for thefirst-order lattice dynamical systems with both deterministic non-autonomousforcing terms and multiplicative white noise. Our results recover many existingones on the existences of pullback attractors for lattice dynamical systemswith autonomous terms or white noises.