Non--autonomous and random attractors for delay random semilinear equations without uniqueness

We first prove the existence and uniqueness of pullback and randomattractors for abstract multi-valued non-autonomous and randomdynamical systems. The standard assumption of compactness of thesesystems can be replaced by the assumption of asymptoticcompactness. Then, we apply the abstract theory to handle a randomreaction-diffusion equation with memory or delay terms which canbe considered on the complete past defined by R⁻. Inparticular, we do not assume the uniqueness of solutions of theseequations.