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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
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Category: math
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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
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Date available: 2021-03-05T10:33:45Z
Last updated: 2021-11-01
Stable URL: http://hdl.handle.net/10338.dmlcz/148717
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