| Title:
|
Asymptotic behaviour of a difference equation with complex-valued coefficients (English) |
| Author:
|
Kalas, Josef |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
311-323 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The asymptotic behaviour for solutions of a difference equation $z_n = f(n,z_n)$, where the complex-valued function $f(n,z)$ is in some meaning close to a holomorphic function $h$, and of a Riccati difference equation is studied using a Lyapunov function method. The paper is motivated by papers on the asymptotic behaviour of the solutions of differential equations with complex-valued right-hand sides. (English) |
| Keyword:
|
difference equations |
| Keyword:
|
asymptotic behaviour |
| Keyword:
|
Lyapunov functions |
| MSC:
|
39A11 |
| idZBL:
|
Zbl 1122.39006 |
| idMR:
|
MR2188386 |
| . |
| Date available:
|
2008-06-06T22:46:22Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107961 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Kalas J.: Asymptotic behaviour of the system of two differential equations.Arch. Math. (Brno) 11 (1975), 175–186. MR 0412530 |
| Reference:
|
[4] Kalas J.: Asymptotic behaviour of the solutions of the equation $dz/dt=f(t,z)$ with a complex-valued function $f$.Qualitative theory of differential equations, Vol. I, II (Szeged, 1979), pp. 431–462, Colloq. Math. Soc. János Bolyai, 30, North-Holland, Amsterdam-New York, 1981. MR 0680606 |
| 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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|
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