On the dynamics generated by a class of functional evolution inclusions (Q1947290)

This article concerns a class of functional evolution inclusions of the form \[ u'(t)+Au(t)\ni f(t),~~t\in [0,T], \] \[ f(t)\in F(u(t),u_t), \] \[ u_t(s)=u(t+s),\,\,u(s)=\phi (s), \,\,s\in [-h,0], \] where \(A\) is an \(m\)-accretive operator on a Banach space \(X\). The goal of this paper is to obtain a global attractor for the above system when the semigroup generated by \(A\) is equicontinuous only, without a compactness assumption on \(A\). The approach is based on the measure of noncompactness.