| Title:
|
Neutral set differential equations (English) |
| Author:
|
Abbas, Umber |
| Author:
|
Lupulescu, Vasile |
| Author:
|
O'Regan, Donald |
| Author:
|
Younus, Awais |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
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65 |
| Issue:
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3 |
| Year:
|
2015 |
| Pages:
|
593-615 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to establish an existence and uniqueness result for a class of the set functional differential equations of neutral type\begin {equation*} \begin {cases} D_{H}X(t)=F(t,X_{t},D_{H}X_{t}), \\ \kern .25em X|_{[-r,0]}=\Psi , \end {cases} \end {equation*} where $F\colon [0,b]\times \mathcal {C}_{0}\times \mathfrak {L}_{0}^{1}\rightarrow K_{c}(E)$ is a given function, $K_{c}(E)$\ is the family of all nonempty compact and convex subsets of a separable Banach space $E$, $\mathcal {C}_{0}$ denotes the space of all continuous set-valued functions $X$ from $[-r,0]$ into $K_{c}(E)$, $\mathfrak {L}_{0}^{1}$ is\ the space of all integrally bounded set-valued functions $X\colon [-r,0]\rightarrow K_{c}(E)$, $\Psi \in \mathcal {C}_{0}$\ and $D_{H}$ is the Hukuhara derivative. The continuous dependence of solutions on initial data and parameters is also studied. (English) |
| Keyword:
|
neutral type |
| Keyword:
|
existence |
| Keyword:
|
uniqueness |
| Keyword:
|
continous dependence |
| MSC:
|
34A12 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 06537683 |
| idMR:
|
MR3407596 |
| DOI:
|
10.1007/s10587-015-0199-9 |
| . |
| Date available:
|
2015-10-04T18:01:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144434 |
| . |
| Reference:
|
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