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ArticleOriginal scientific text

Title

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

Authors 1, 2, 3

Affiliations

  1. Istituto di Matematica Applicata, Facoltà di Architettura, Università di Firenze, Italy
  2. Department of Physics and Mathematics, Voronezh Pedagogical University, Russia
  3. Dipartimento di Sistemi e Informatica, Università di Firenze, via S. Marta 3, 50139 Firenze, Italy

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 Rδ-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].

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Banach Center Publications
1996/35/1
Export to PBN, Opens in new tab
Pages:
159-169
Main language of publication
English
Published
1996
Exact and natural sciences