Long-time behavior of stochastic reaction-diffusion equation with multiplicative noise

In this paper, we study the dynamical behavior of the solution for the stochastic reaction-diffusion equation with the nonlinearity satisfying the polynomial growth of arbitrary order p >= 2 and any space dimensionN. Based on the inductive principle, the higher-order integrability of the difference of the solutions near the initial data is established, and then the (norm-to-norm) continuity of solutions with respect to the initial data in H-0(1)(U)is first obtained. As an application, we show the existence of(L-2(U),L-p(U)) and (L-2(U),H-0(1)(U))-pullback random attractors, respectively.