| Title:
|
On the dimension of the solution set to the homogeneous linear functional differential equation of the first order (English) |
| Author:
|
Domoshnitsky, Alexander |
| Author:
|
Hakl, Robert |
| Author:
|
Půža, Bedřich |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
1033-1053 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Consider the homogeneous equation $$ u'(t)=\ell (u)(t)\qquad \mbox {for a.e. } t\in [a,b] $$ where $\ell \colon C([a,b];\Bbb R)\to L([a,b];\Bbb R)$ is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations. (English) |
| Keyword:
|
functional differential equation |
| Keyword:
|
boundary value problem |
| Keyword:
|
differential inequality |
| Keyword:
|
solution set |
| MSC:
|
34K06 |
| MSC:
|
34K10 |
| idZBL:
|
Zbl 1274.34184 |
| idMR:
|
MR3010255 |
| DOI:
|
10.1007/s10587-012-0062-1 |
| . |
| Date available:
|
2012-11-10T21:40:36Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143043 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
