On the upper semicontinuity of pullback attractors for multi-valued noncompact random dynamical systems

Abstract

In this paper, we first present someconditions for the upper semicontinuity of pullback attractors formulti-valued noncompact random dynamical systems with smallperturbations. Then we establish the upper semicontinuity of pullback attractors for nonautonomous andstochastic reaction-diffusion delay equationsdefined on $\mathbb{R}^n$ with small time delay perturbation for which uniqueness of solutionsneed not hold. Finally, we prove the existence and uppersemicontinuity of pullback attractors for nonautonomous andstochastic nonclassical diffusion equations with polynomial growth nonlinearity of arbitrary order and without the uniqueness of solutions.