# Publishing house / Banach Center Publications / All volumes

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

### Volume 35 / 1996

Banach Center Publications 35 (1996), 159-169 DOI: 10.4064/-35-1-159-169

#### Abstract

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,x_t) 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].

#### Authors

• Giuseppe Conti
• Valeri Obukhovskiĭ
• Pietro Zecca

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