| Title:
|
Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term (English) |
| Author:
|
Andres, Jan |
| Author:
|
Bersani, Alberto Maria |
| Author:
|
Radová, Lenka |
| Language:
|
English |
| Journal:
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Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
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0231-9721 |
| Volume:
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45 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
7-29 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Almost-periodic solutions in various metrics (Stepanov, Weyl, Besicovitch) of higher-order differential equations with a nonlinear Lipschitz-continuous restoring term are investigated. The main emphasis is focused on a Lipschitz constant which is the same as for uniformly almost-periodic solutions treated in [A1] and much better than those from our investigations for differential systems in [A2], [A3], [AB], [ABL], [AK]. The upper estimates of $\varepsilon $ for $\varepsilon $-almost-periods of solutions and their derivatives are also deduced under various restrictions imposed on the constant coefficients of the linear differential operator on the left-hand side of the given equation. Besides the existence, uniqueness and localization of almost-periodic solutions and their derivatives are established. (English) |
| Keyword:
|
Almost-periodic solutions |
| Keyword:
|
various metrics |
| Keyword:
|
higher-order differential equation |
| Keyword:
|
nonlinear restoring term |
| Keyword:
|
existence and uniqueness criteria |
| MSC:
|
34C15 |
| MSC:
|
34C27 |
| MSC:
|
42A75 |
| idZBL:
|
Zbl 1128.34029 |
| idMR:
|
MR2321293 |
| . |
| Date available:
|
2009-08-21T07:05:17Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133445 |
| . |
| 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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