Kapustyan O. Global attractors for nonautonomous multivalued dynamical systems

The thesis is devoted to construction of the theory of global attractors of multivalued nonautonomous and random dynamical systems. An abstract theory are developed in general topological spaces. The properties of compactness, invariance, connectedness, stability and dependence on parameter are investigated. The theorems on existence of global attractor for some classes of nonlinear evolution equations and inclusions with trans-lation-compact in time right-hand part, for some cascade systems and for evolution equations and inclusions with impulsive effects at fixed moments of time are proved. An abstract theory of random attractors for multivalued random dynamical systems are investigated. Results about existence of random attractor for some classes of randomly perturbed evolution systems are obtained.