Stable Sets, Attracting Sets, and Attractors of Semidynamical Systems in Nonlocally Compact Metric Spaces

摘要

We single out a class of semidynamical systems that have the same properties as dynamical systems in locally compact spaces and in particular include partial differential equations of parabolic type and delay differential equations. We show that the Ura criterion for the stability of a set, the Zubov criterion for the asymptotic stability of a set, and the theorem on the minimal asymptotically stable set hold for this class of systems, and we derive conditions for the existence of an absorbing set and an attractor.