Random dynamics of stochastic p-Laplacian equations on RN with an unbounded additive noise

This article is concerned with the random dynamics of solutions of the non-autonomous parabolic p-Laplacian equations on RN driven by an unbounded additive noise, where the nonlinearity has a (p,q)-growth exponents including the general polynomial-type functions. Firstly by using an inductive method, we establish the higher-order integrability of difference of solutions near the initial time for arbitrary space dimension. Secondly based on this very estimate, the asymptotical compactness of solutions in Lp(RN)∩Lq(RN) for any p,q≥2 is proved by a new technique instead of the usual truncation estimate method, and then we obtain the existence of pullback attractor in Lp(RN)∩Lq(RN) for p-Laplacian equations with an unbounded additive noise. Thirdly we prove that the obtained L2-pullback attractor is attracting and translation bounded in Lδ(RN) topology for any δ∈[2,∞) and arbitrary space dimension N,N≥1.