Weak Pullback Mean Random Attractors for Stochastic $p$-Laplacian Equation in Higher Order Bochner Spaces

We consider the non-autonomous p-Laplacian equation in higher order Bochner spaces. By using the higher-order energy estimates and the framework of mean random dynamical systems, we establish the existence and uniqueness of weak pullback mean random attractors for the deterministic p-Laplacian equation with random initial data as well as the stochastic p-Laplacian equation with monotone drift and nonlinear diffusion terms.