Differential equations with set-valued solutions

Abstract

Some special space of convex compact sets is considered and notions of a derivative and an integral for multivalued mapping different from already known ones are introduced. The differential equation with multivalued right-hand side satisfying the Caratheodory conditions is also considered and the theorems on the existence and uniqueness of its solutions are proved. In contrast to O. Kaleva's approach, the given approach enables one to consider fuzzy differential equations as usual differential equations with multivalued solutions.