# 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

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topConti, 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 -

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