Title:
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Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, II (English) |
Author:
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Naito, Manabu |
Language:
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English |
Journal:
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Archivum Mathematicum |
ISSN:
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0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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57 |
Issue:
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1 |
Year:
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2021 |
Pages:
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41-60 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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:
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asymptotic behavior |
Keyword:
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nonoscillatory solution |
Keyword:
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half-linear differential equation |
Keyword:
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Hardy-type inequality |
MSC:
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26D10 |
MSC:
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34C10 |
MSC:
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34C11 |
idZBL:
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Zbl 07332703 |
idMR:
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MR4260839 |
DOI:
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10.5817/AM2021-1-41 |
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Date available:
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2021-03-05T10:33:45Z |
Last updated:
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2021-11-01 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/148717 |
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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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