Existence of Random Attractors for a Class of Second-Order Lattice Dynamical Systems with Brownian Motions

摘要

This paper is concerned with the random attractors for a class of second-order stochastic lattice dynamical systems. We first prove the uniqueness and existence of the solutions of second-order stochastic lattice dynamical systems in the space F = l(lambda)(2) x l(2). Then, by proving the asymptotic compactness of the random dynamical systems, we establish the existence of the global random attractor. The system under consideration is quite general, and many existing results can be regarded as the special case of our results.