Abstract
It is known that a Frechet space F can be realized as a projective limit of a sequence of Banach spaces Ei. The space Kc(F) of all compact, convex subsets of a Frechet space, F, is realized as a projective limit of the semilinear metric spacesKc(E). Using the notion of Hukuhara derivative for maps with values inKc(F), we prove the local and global existence theorems for an initial value problem associated with a set differential equation.
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