Existence and Topological Properties of Solution Sets for Differential Inclusions with Delay

Adel Mahmoud Gomaa. "Existence and Topological Properties of Solution Sets for Differential Inclusions with Delay." Commentationes Mathematicae 48.1 (2008): null. <http://eudml.org/doc/291848>.

@article{AdelMahmoudGomaa2008,
abstract = {We consider the problem $\dot\{x\}(t) \in A(t)x(t) + F (t, θ_t x))$ a.e. on $[0, b]$, $x = \kappa $ on $[-d, 0]$ in a Banach space $E$, where $\kappa $ belongs to the Banach space, $C_E ([-d, 0])$, of all continuous functions from $[-d, 0]$ into $E$. A multifunction $F$ from $[0, b] \times C_E ([-d, 0])$ into the set, $P_\{f_c\} (E)$, of all nonempty closed convex subsets of $E$ is weakly sequentially hemi-continuous, $θ_t x(s) = x(t + s)$ for all $s \in [-d, 0]$ and $\lbrace A(t) : 0 \le t \le b\rbrace $ is a family of densely defined closed linear operators generating a continuous evolution operator $S(t, s)$. Under a generalization of the compactness assumptions, we prove an existence result and give some topological properties of our solution sets that generalizes earlier theorems by Papageorgiou, Rolewicz, Deimling, Frankowska and Cichoń.},
author = {Adel Mahmoud Gomaa},
journal = {Commentationes Mathematicae},
keywords = {Differential inclusions; mutifunctions; measures of noncompactness; delay},
language = {eng},
number = {1},
pages = {null},
title = {Existence and Topological Properties of Solution Sets for Differential Inclusions with Delay},
url = {http://eudml.org/doc/291848},
volume = {48},
year = {2008},
}

TY - JOUR
AU - Adel Mahmoud Gomaa
TI - Existence and Topological Properties of Solution Sets for Differential Inclusions with Delay
JO - Commentationes Mathematicae
PY - 2008
VL - 48
IS - 1
SP - null
AB - We consider the problem $\dot{x}(t) \in A(t)x(t) + F (t, θ_t x))$ a.e. on $[0, b]$, $x = \kappa $ on $[-d, 0]$ in a Banach space $E$, where $\kappa $ belongs to the Banach space, $C_E ([-d, 0])$, of all continuous functions from $[-d, 0]$ into $E$. A multifunction $F$ from $[0, b] \times C_E ([-d, 0])$ into the set, $P_{f_c} (E)$, of all nonempty closed convex subsets of $E$ is weakly sequentially hemi-continuous, $θ_t x(s) = x(t + s)$ for all $s \in [-d, 0]$ and $\lbrace A(t) : 0 \le t \le b\rbrace $ is a family of densely defined closed linear operators generating a continuous evolution operator $S(t, s)$. Under a generalization of the compactness assumptions, we prove an existence result and give some topological properties of our solution sets that generalizes earlier theorems by Papageorgiou, Rolewicz, Deimling, Frankowska and Cichoń.
LA - eng
KW - Differential inclusions; mutifunctions; measures of noncompactness; delay
UR - http://eudml.org/doc/291848
ER -