The functional differential inclusions with impulses and with the right-hand side not necessarily convex-valued with respect to switching

The Cauchy problem for the functional differential inclusion with Volterra's multivalued map not necessarily convex-valued with respect to switching and with impulses is considered. For this problem, the definition of a generalized solution is introduced, and the questions of existence and extendibility of generalized solutions are studied. Notions of a near-realization and realization of the distance to an arbitrary summable function by the set of generalized solutions are formulated. For a set of generalized solutions of functional differential inclusions with impulses and with multivalued map not necessarily convex-valued with respect to switching, estimations are found similar to A. F. Filippov's estimations. The generalized principle of density is proved.