Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equations
Accurate asymptotic formulas for regularly varying solutions of the second order half-linear differential equation \begin{equation*} (|x'|^{\alpha}\textrm{sgn}\; x')' + q(t)|x|^{\alpha}\textrm{sgn}\; x = 0, \end{equation*} will be established explicitly, depending on the rate of deca...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-08-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4566 |
| _version_ | 1797830564779130880 |
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| author | Takaŝi Kusano Jelena Manojlović |
| author_facet | Takaŝi Kusano Jelena Manojlović |
| author_sort | Takaŝi Kusano |
| collection | DOAJ |
| description | Accurate asymptotic formulas for regularly varying solutions of the second order half-linear differential equation
\begin{equation*}
(|x'|^{\alpha}\textrm{sgn}\; x')' + q(t)|x|^{\alpha}\textrm{sgn}\; x = 0,
\end{equation*}
will be established explicitly, depending on the rate of decay toward zero of the function
\begin{equation*}Q_c(t) = t^{\alpha}\int_t^{\infty}q(s)ds - c\end{equation*}
as $t\to\infty$, where $c<\alpha^\alpha(\alpha+1)^{-\alpha-1}$. |
| first_indexed | 2024-04-09T13:38:06Z |
| format | Article |
| id | doaj.art-35056b7b33874584a842d7df8ed014a9 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:06Z |
| publishDate | 2016-08-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-35056b7b33874584a842d7df8ed014a92023-05-09T07:53:06ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-08-0120166212410.14232/ejqtde.2016.1.624566Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equationsTakaŝi Kusano0Jelena Manojlović1Hiroshima University, Higashi-Hiroshima, JapanUniversity of Nis, Nis, SerbiaAccurate asymptotic formulas for regularly varying solutions of the second order half-linear differential equation \begin{equation*} (|x'|^{\alpha}\textrm{sgn}\; x')' + q(t)|x|^{\alpha}\textrm{sgn}\; x = 0, \end{equation*} will be established explicitly, depending on the rate of decay toward zero of the function \begin{equation*}Q_c(t) = t^{\alpha}\int_t^{\infty}q(s)ds - c\end{equation*} as $t\to\infty$, where $c<\alpha^\alpha(\alpha+1)^{-\alpha-1}$.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4566half-linear differential equationsregularly varying solutionsslowly varying solutionsasymptotic behavior of solutionspositive solutions |
| spellingShingle | Takaŝi Kusano Jelena Manojlović Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equations Electronic Journal of Qualitative Theory of Differential Equations half-linear differential equations regularly varying solutions slowly varying solutions asymptotic behavior of solutions positive solutions |
| title | Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equations |
| title_full | Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equations |
| title_fullStr | Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equations |
| title_full_unstemmed | Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equations |
| title_short | Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equations |
| title_sort | precise asymptotic behavior of regularly varying solutions of second order half linear differential equations |
| topic | half-linear differential equations regularly varying solutions slowly varying solutions asymptotic behavior of solutions positive solutions |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4566 |
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