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This thesis is concerned with the asymptotic behavior of solutions ofstochastic $p$-Laplace equations driven by non-autonomous forcing on$\mathbb{R}^n$. Two cases are studied, with additive and multiplicative noiserespectively. Estimates on the tails of solutions are used to overcome thenon-compactness of Sobolev embeddings on unbounded domains, and proveasymptotic compactness of solution operators in $L^2(\mathbb{R}^n)$. Using thisresult we prove the existence and uniqueness of random attractors in each case.Additionally, we show the upper semicontinuity of the attractor for themultiplicative noise case as the intensity of the noise approaches zero.

Asymptotic Dynamics of Stochastic $p$-Laplace Equations on Unbounded Domains