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Generalized solutions of functional differential inclusions. (English) Zbl 1149.34037

Summary: We consider the initial value problem for a functional differential inclusion with a Volterra multivalued mapping that is not necessarily decomposable in \(L_{1}^{n}[a,b]\). 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.

MSC:

34K05 General theory of functional-differential equations
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