We consider the problem [formula] in a Banach space E, where belongs to the Banach space, CE([-d, 0]), of all continuous functions from [-d, 0] into E. A multifunction F from [0, b] × CE([-d, 0]) into the set, Pfc(E), of all nonempty closed convex subsets of E is weakly sequentially hemi-continuous, tx(s) = x(t + s) for all s 2 [-d, 0] and {A(t) : 0 6 t 6 b} is a family of densely defined closed linear operators generating a continuous evolution operator S(t, s). Under a generalization of the compactness assumptions, we prove an existence result and give some topological properties of our solution sets that generalizes earlier theorems by Papageorgiou, Rolewicz, Deimling, Frankowska and Cichon..
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