Existence and General Properties of Solutions of Discontinuous Systems

Abstract

Various definitions of solutions of differential equations and systems with discontinuous right-hand sides are considered for the cases where, by contrast with Chapter 1, the right-hand sides are not continuous in x. The range of applicability of different definitions is indicated. For differential equations with discontinuous right-hand sides and for differential inclusions, existence of solutions is proved and the properties of these solutions are analyzed; in particular, the dependence of solutions on initial data and on right-hand sides of equations, and the properties of integral funnels are examined.