Differential Inclusions. Existence of Solutions

Abstract

In this Chapter questions of the existence of classical, regular, and Caratheodory type of solutions of a differential inclusion with non-convex right hand side are considered. The solutions of the differential inclusion are sought as continuous selectors of a solution of a multi-valued differential equation generated by a differential inclusion, and the interval of their existence concides with that of a multi-valued differential equation. The proof of the existence of solutions of a differential inclusion with non-convex right hand side is based on theorems about continuous selectors with certain properties in corresponding functional spaces for multi-functions with non-convex values, the classical Tychonov-Schauder theorem of a fixed point, and on the representation of the solution of a multi-valued equation as a convex compact set of its continuous selectors.