| Title:
|
An almost-periodicity criterion for solutions of the oscillatory differential equation $y''=q(t)y$ and its applications (English) |
| Author:
|
Staněk, Svatoslav |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
229-241 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The linear differential equation $(q):y''=q(t)y$ with the uniformly almost-periodic function $q$ is considered. Necessary and sufficient conditions which guarantee that all bounded (on $\mathbb{R}$) solutions of $(q)$ are uniformly almost-periodic functions are presented. The conditions are stated by a phase of $(q)$. Next, a class of equations of the type $(q)$ whose all non-trivial solutions are bounded and not uniformly almost-periodic is given. Finally, uniformly almost-periodic solutions of the non-homogeneous differential equations $y''=q(t)y+f(t)$ are considered. The results are applied to the Appell and Kummer differential equations. (English) |
| Keyword:
|
linear second-order differential equation |
| Keyword:
|
Appell equation |
| Keyword:
|
Kummer equation |
| Keyword:
|
uniformly almost-periodic solution |
| Keyword:
|
bounded solution |
| Keyword:
|
phase |
| MSC:
|
34C27 |
| idZBL:
|
Zbl 1117.34043 |
| idMR:
|
MR2164672 |
| . |
| Date available:
|
2008-06-06T22:46:02Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107953 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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