Title:
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Oscillation of third order differential equation with damping term (English) |
Author:
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Bartušek, Miroslav |
Author:
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Došlá, Zuzana |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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65 |
Issue:
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2 |
Year:
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2015 |
Pages:
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301-316 |
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 study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term $$ x'''(t)+q(t)x'(t)+r(t)|x|^{\lambda }(t)\mathop {\rm sgn} x(t)=0 ,\quad t\geq 0. $$ We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case $\lambda \leq 1$ and if the corresponding second order differential equation $h''+q(t)h=0$ is oscillatory, we also study Kneser solutions vanishing at infinity and the existence of oscillatory solutions. (English) |
Keyword:
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third order nonlinear differential equation |
Keyword:
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vanishing at infinity solution |
Keyword:
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Kneser solution |
Keyword:
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oscillatory solution |
MSC:
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34C10 |
MSC:
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34C15 |
idZBL:
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Zbl 06486947 |
idMR:
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MR3360427 |
DOI:
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10.1007/s10587-015-0176-3 |
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Date available:
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2015-06-16T17:31:56Z |
Last updated:
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2020-07-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/144270 |
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Reference:
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