Global attractors for non-autonomous multivalued dynamical systems associated with double obstacle problems

Abstract

In this paper we consider double obstacle problems including regional economic growth models. Unfortunately, by prescribed double obstacles, our problems lose the uniqueness of solutions. So, our problems have multiple solutions for a given initial value. Hence, the associated dynamical systems are multivalued. In this paper we shall consider the large-time behaviour of multiple solutions from the viewpoint of attractors. Namely, the main object of this paper is to construct the global attractors for non-autonomous multivalued dynamical systems associated with double obstacle problems.