The definitions and most results of Section 1 are classical. Some related material appears in the book by Berge . Theorem 1.2 is stated without proof (and without the assumption of completeness of Y) in Choquet . For the history of the concepts of continuity of set valued maps we refer to the forthcoming book by Rockafellar and Wets. For Theorem 2.2 we refer to the book by Spanier . Proposition 2.2 is taken from Aubin [1979c], while Proposition 2.3 comes from the book by Ekeland and Teman . Theorems 2.4 and 2.5 are well known theorems from Berge . The important results of Section 3 were obtained independently by Robinson [1976a] and Ursescu .
KeywordsDifferential Inclusion Maximal Monotone Infinite Dimensional Banach Space Differential Variational Inequality Convex Image
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