On the topological structure of the solution set for a semilinear ffunctional-differential inclusion in a Banach space

Conti, Giuseppe ; Obukhovskiĭ, Valeri ; Zecca, Pietro

Banach Center Publications, Tome 37 (1996), p. 159-169 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper we show that the set of all mild solutions of the Cauchy problem for a functional-differential inclusion in a separable Banach space E of the form x’(t) ∈ A(t)x(t) + F(t,xt) is an $R_δ$-set. Here A(t) is a family of linear operators and F is a Carathéodory type multifunction. We use the existence result proved by V. V. Obukhovskiĭ [22] and extend theorems on the structure of solutions sets obtained by N. S. Papageorgiou [23] and Ya. I. Umanskiĭ [32].

Détail

Publié le : 1996-01-01

Zbl 0845.34027

EUDML-ID : urn:eudml:doc:251335

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