In this article, we prove the existence of a random attractor for stochastic nonclassical diffusion equations on unbounded domains, and the asymptotic compactness of the random dynamical system is established by a tail-estimates method.Mathematics Subject Classification. 35B41, 35Q35.

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In this paper, we consider the existence of positive solutions of a class of discrete difference systems, λ is a positive parameter. We prove the existence of a large positive solution for λ large enough under suitable assumptions on f and g. The proof of our main result is based upon the Schauder's fixed point theorem.Mathematics Subject Classification: 34B18