| Title:
|
On the instability of linear nonautonomous delay systems (English) |
| Author:
|
Naulin, Raúl |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
497-514 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The unstable properties of the linear nonautonomous delay system $x^{\prime }(t)=A(t)x(t)+B(t)x(t-r(t))$, with nonconstant delay $r(t)$, are studied. It is assumed that the linear system $y^{\prime }(t)=(A(t)+B(t))y(t)$ is unstable, the instability being characterized by a nonstable manifold defined from a dichotomy to this linear system. The delay $r(t)$ is assumed to be continuous and bounded. Two kinds of results are given, those concerning conditions that do not include the properties of the delay function $r(t)$ and the results depending on the asymptotic properties of the delay function. (English) |
| Keyword:
|
Liapounov instability |
| Keyword:
|
$h$-instability |
| Keyword:
|
instability of delay equations |
| Keyword:
|
nonconstant delays |
| MSC:
|
34D05 |
| MSC:
|
34D09 |
| MSC:
|
34D20 |
| MSC:
|
34K06 |
| MSC:
|
34K20 |
| idZBL:
|
Zbl 1080.34543 |
| idMR:
|
MR2000048 |
| . |
| Date available:
|
2009-09-24T11:03:48Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127818 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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|
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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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| . |
