Properties of Solutions

Abstract

In this Chapter we study interrelationships between a set of all, of some type or other, solutions of a differential inclusion with non-convex right hand side and a set of all, of the same type of solutions of a differential inclusions with convexified right hand side. It is shown that each, of some type or other, solution of the differential inclusion is a selector of the same solution of a multi-valued differential equation generated by a differential inclusion. We have established the density and co-density of a set of all, of some type or other, solutions of a differential inclusion with non-convex right hand side in a set of all Caratheodory type of solutions of a differential inclusion with convexified right hand side. In addition, in this Section properties of a set of all solutions of a differential inclusion such as the compactness, the connectedness and the dependence on initial conditions and parameters, are considered.