Generalized solutions of functional differential inclusions
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.
scientific article; zbMATH DE number 5313160
scientific article