| Title:
|
Asymptotic properties of solutions of nonautonomous difference equations (English) |
| Author:
|
Migda, Janusz |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
1-11 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Asymptotic properties of solutions of difference equation of the form
\[ \Delta ^m x_n=a_n\varphi _n(x_{\sigma (n)})+b_n \]
are studied. Conditions under which every (every bounded) solution of the equation $\Delta ^m y_n=b_n$ is asymptotically equivalent to some solution of the above equation are obtained. Moreover, the conditions under which every polynomial sequence of degree less than $m$ is asymptotically equivalent to some solution of the equation and every solution is asymptotically polynomial are obtained. The consequences of the existence of asymptotically polynomial solution are also studied. (English) |
| Keyword:
|
difference equation |
| Keyword:
|
asymptotic behavior |
| Keyword:
|
asymptotically polynomial solution |
| MSC:
|
39A10 |
| idZBL:
|
Zbl 1240.39009 |
| idMR:
|
MR2644450 |
| . |
| Date available:
|
2010-04-22T10:40:10Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/139989 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Migda, J.: Asymptotic properties of solutions of higher order difference equations.submitted. Zbl 0702.39002 |
| 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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| . |
