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

Giuseppe Conti; Valeri Obukhovskiĭ; Pietro Zecca

Banach Center Publications (1996)

  • Volume: 35, Issue: 1, page 159-169
  • ISSN: 0137-6934

Abstract

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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].

How to cite

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Conti, Giuseppe, Obukhovskiĭ, Valeri, and Zecca, Pietro. "On the topological structure of the solution set for a semilinear ffunctional-differential inclusion in a Banach space." Banach Center Publications 35.1 (1996): 159-169. <http://eudml.org/doc/251335>.

@article{Conti1996,
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,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].},
author = {Conti, Giuseppe, Obukhovskiĭ, Valeri, Zecca, Pietro},
journal = {Banach Center Publications},
keywords = {mild solutions; Cauchy problem; functional-differential inclusion; Banach space; -set},
language = {eng},
number = {1},
pages = {159-169},
title = {On the topological structure of the solution set for a semilinear ffunctional-differential inclusion in a Banach space},
url = {http://eudml.org/doc/251335},
volume = {35},
year = {1996},
}

TY - JOUR
AU - Conti, Giuseppe
AU - Obukhovskiĭ, Valeri
AU - Zecca, Pietro
TI - On the topological structure of the solution set for a semilinear ffunctional-differential inclusion in a Banach space
JO - Banach Center Publications
PY - 1996
VL - 35
IS - 1
SP - 159
EP - 169
AB - 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].
LA - eng
KW - mild solutions; Cauchy problem; functional-differential inclusion; Banach space; -set
UR - http://eudml.org/doc/251335
ER -

References

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