The Cauchy problem for an inclusion in Banach spaces and distribution spaces.
Let , and be normed linear spaces with and linear relations, i.e. setvalued maps. We seek necessary and sufficient conditions that would ensure that . First, we cast the concepts of relative boundedness and co-continuity in the set valued case and establish a duality. This duality turns out to be similar to the one that exists for densely defined linear operators and is then used to establish the necessary and sufficient conditions. These conditions are similar to those for the single...