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.


34K05 General theory of functional-differential equations
Full Text: DOI EuDML


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