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Generalized Solutions of Functional Differential Inclusions

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  • Anna Machina
  • Aleksander Bulgakov
  • Anna Grigorenko

Abstract

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.

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Handle: RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:829701
DOI: 10.1155/2008/829701
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