Asymptotic Behaviour of Monotone Multi-Valued Dynamical Systems

Abstract

We introduce the concept of a monotone multi-valued semi- ow as an order-preserving map. This de nition is motivated by the applications in the theory of di¤erential equations without uniqueness of solutions. For an order preserving multi-valued semi- ow we prove several results on the structure of the global attractor. Some applications to models governed by ordinary di¤erential equations and delay equations with continuous right-hand side are presented. In particular, the abstract results are applied to a biochemical control circuit.