Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variation
The asymptotic behavior of solutions of the odd-order differential equation of Emden-Fowler type $$ x^{(2n+1)}(t) + q(t)|x(t)|^{\gamma}\textrm{sgn}\;x(t)=0 , $$ is studied in the framework of regular variation, under the assumptions that $0<\gamma<1$ and $q(t):[a,\infty)\to(0,\infty)$ is regul...
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| Format: | Article |
| Language: | English |
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University of Szeged
2012-06-01
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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=1444 |
| _version_ | 1797830630769164288 |
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| author | Takaŝi Kusano Jelena Manojlović |
| author_facet | Takaŝi Kusano Jelena Manojlović |
| author_sort | Takaŝi Kusano |
| collection | DOAJ |
| description | The asymptotic behavior of solutions of the odd-order differential equation of Emden-Fowler type
$$
x^{(2n+1)}(t) + q(t)|x(t)|^{\gamma}\textrm{sgn}\;x(t)=0 ,
$$
is studied in the framework of regular variation, under the assumptions that $0<\gamma<1$ and $q(t):[a,\infty)\to(0,\infty)$ is regularly varying function. It is shown that
complete and accurate information can be acquired about the existence of all possible positive solutions and their asymptotic behavior at infinity. |
| first_indexed | 2024-04-09T13:40:13Z |
| format | Article |
| id | doaj.art-293fb60573b14f29a5b62ff5aea69832 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:40:13Z |
| publishDate | 2012-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-293fb60573b14f29a5b62ff5aea698322023-05-09T07:53:02ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752012-06-0120124512310.14232/ejqtde.2012.1.451444Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variationTakaŝi Kusano0Jelena Manojlović1Hiroshima University, Higashi-Hiroshima, JapanUniversity of Nis, Nis, SerbiaThe asymptotic behavior of solutions of the odd-order differential equation of Emden-Fowler type $$ x^{(2n+1)}(t) + q(t)|x(t)|^{\gamma}\textrm{sgn}\;x(t)=0 , $$ is studied in the framework of regular variation, under the assumptions that $0<\gamma<1$ and $q(t):[a,\infty)\to(0,\infty)$ is regularly varying function. It is shown that complete and accurate information can be acquired about the existence of all possible positive solutions and their asymptotic behavior at infinity.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1444odd-order differential equationintermediate solutionregularly varying functionslowly varying functionasymptotic behavior of solutions |
| spellingShingle | Takaŝi Kusano Jelena Manojlović Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variation Electronic Journal of Qualitative Theory of Differential Equations odd-order differential equation intermediate solution regularly varying function slowly varying function asymptotic behavior of solutions |
| title | Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variation |
| title_full | Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variation |
| title_fullStr | Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variation |
| title_full_unstemmed | Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variation |
| title_short | Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variation |
| title_sort | asymptotic behavior of positive solutions of odd order emden fowler type differential equations in the framework of regular variation |
| topic | odd-order differential equation intermediate solution regularly varying function slowly varying function asymptotic behavior of solutions |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1444 |
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