| Title:
|
Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, II (English) |
| Author:
|
Naito, Manabu |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
41-60 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the half-linear differential equation of the form \[ (p(t)|x^{\prime }|^{\alpha }\mathrm{sgn}\,x^{\prime })^{\prime } + q(t)|x|^{\alpha }\mathrm{sgn}\,x = 0\,, \quad t \ge t_{0} \,, \] under the assumption that $p(t)^{-1/\alpha }$ is integrable on $[t_{0}, \infty )$. It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as $t \rightarrow \infty $. (English) |
| Keyword:
|
asymptotic behavior |
| Keyword:
|
nonoscillatory solution |
| Keyword:
|
half-linear differential equation |
| Keyword:
|
Hardy-type inequality |
| MSC:
|
26D10 |
| MSC:
|
34C10 |
| MSC:
|
34C11 |
| idZBL:
|
Zbl 07332703 |
| idMR:
|
MR4260839 |
| DOI:
|
10.5817/AM2021-1-41 |
| . |
| Date available:
|
2021-03-05T10:33:45Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148717 |
| . |
| 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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| . |
