Fundamental theory of contingent differential equations in Banach space

Abstract

For a contingent differential equation that takes values in the closed, convex, nonempty subsets of a Banach space <italic>E</italic> , we prove an existence theorem and we investigate the extendability of solutions and the closedness and continuity properties of solution funnels. We consider first a space <italic>E</italic> that is separable and reflexive and then a space <italic>E</italic> with a separable second dual space. We also consider the special case of a point-valued or ordinary differential equation.