Random attractors for stochastic semilinear degenerate parabolic equations with delay

In this paper, we consider a stochastic semilinear degenerate parabolic equation with delay in a bounded domain in RN and the nonlinearity satisfying an arbitrary polynomial growth condition. The random dynamical system generated by the equation is shown to have a random attractor in C([−τ,0],Lp(O)∩D01(O,σ)), which is a compact and invariant tempered set and attracts every tempered random subset of C([−τ,0],L2(O)) in the topology of C([−τ,0],Lp(O)). In a particular case, the random attractor consists of singleton sets (i.e., a random fixed point), which generates an exponentially stable non-trivial stationary solution. This theoretical result improves some recent ones for stochastic semilinear degenerate parabolic equations. •A stochastic semilinear degenerate parabolic equation with delay in a bounded domain is studied.•The existence and regularity of pullback attractors is studied extensively.•The continuity of the solution semigroup in C([−τ,0],Lp(O)) with p≠2 is investigated.