| Abstract: | In Bressan and Staicu, Set-Valued Anal.2 (1994), 415–437, qualitative properties for solutions of the evolution inclusion   Ax+F(t,x), with A generator of a contractive semigroup and F a lower semicontinuous closed valued multifunction defined on compact subset of R×cl(D(A)), were deduced as corollaries of similar properties for solutions of the evolution inclusion  Ax+G(t,x), where G is upper semicontinuous compact convex valued, obtained from a suitable directionally continuous selection from F.In this paper we prove that the compactness assumption on the domain of F can be avoided. |
