Existence and upper semicontinuity of random attractors for stochastic degenerate parabolic equations with multiplicative noises

The existence and the upper semicontinuity of random attractors in L2(RN)L2(RN) for stochastic semi-linear degenerate parabolic equations with multiplicative noises are obtained. Though the spatial domain is the entire space RN,RN, a compact embedding is applied to get the compactness of random absorbing sets, from which follows the compactness of the system and the precompactness of the union of all perturbed random attractors.