Generalized Solutions of Functional Differential Inclusions

Abstract EN

We consider the initial value problem for a functional differential inclusion with a Volterra multivalued mapping that is not necessarily decomposable in L1n[a,b].

The concept of the decomposable hull of a set is introduced.

Using this concept, we define a generalized solution of such a problem and study its properties.

We have proven that standard results on local existence and continuation of a generalized solution remain true.

The question on the estimation of a generalized solution with respect to a given absolutely continuous function is studied.

The density principle is proven for the generalized solutions.

Asymptotic properties of the set of generalized approximate solutions are studied.