Attractors of asymptotically periodic multivalued dynamical systems governed by time-dependent subdifferentials

We study a nonlinear evolution equation associated with time-dependent subdifferential in a separable Hilbert space. In particular, we consider an asymptotically periodic system, which means that time-dependent terms converge to time-periodic terms as time approaches infinity. Then we consider the large-time behavior of solutions without uniqueness. In such a situation the corresponding dynamical systems are multivalued. In fact, we discuss the stability of multivalued semiflows from the view-point of attractors. Namely, the main object of this paper is to construct a global attractor for asymptotically periodic multivalued dynamical systems, and to discuss the relationship to one for the limiting periodic systems.