Random attractor for stochastic p -Laplacian equations with dynamic boundary conditions driven by nonlinear colored noise

In this paper, we consider the asymptotic behavior of solutions of an evolution equation containing the non-autonomous p-Laplacian equation with polynomial growth nonlinearity of arbitrary order and dynamic boundary conditions driven by nonlinear colored noise. We first prove the existence of weak solutions by the Faedo–Galerkin method, but the uniqueness of solutions cannot be guaranteed due to the lack of Lipschitz continuity of diffusion and nonlinear terms. Then we establish the asymptotic compactness of the corresponding cocycle by Sobolev compactness embedding theorem and the measurability of the random attractor by proving the weak upper semi-continuity of the multi-valued non-autonomous cocycle. Finally, we prove the existence and uniqueness of pullback random attractor for the multi-valued non-autonomous cocycle generated by the solution operator.