Asymptotic and oscillatory behavior of higher order quasilinear delay differential equations
In the paper, we offer such generalization of a lemma due to Philos (and partially Staikos), that yields many applications in the oscillation theory. We present its disposal in the comparison theory and we establish new oscillation criteria for $n-$th order delay differential equation \begin{equati...
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| Format: | Article |
| Language: | English |
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University of Szeged
2012-11-01
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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=1807 |
| _version_ | 1827951325762027520 |
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| author | Blanka Baculíková Jozef Džurina |
| author_facet | Blanka Baculíková Jozef Džurina |
| author_sort | Blanka Baculíková |
| collection | DOAJ |
| description | In the paper, we offer such generalization of a lemma due to Philos (and partially Staikos), that yields many applications in the oscillation theory. We present its disposal in the comparison theory and we establish new oscillation criteria for $n-$th order delay differential equation
\begin{equation*}
\left(r(t)\left[x'(t)\right]^{\gamma}\right)^{(n-1)}+q(t)x^{\gamma}(\tau(t))=0.\tag{$E$}
\end{equation*}
The presented technique essentially simplifies the examination of the higher order differential equations. |
| first_indexed | 2024-04-09T13:40:01Z |
| format | Article |
| id | doaj.art-f420a43b5e2242dea4ab9b0a630a65ce |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:40:01Z |
| publishDate | 2012-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-f420a43b5e2242dea4ab9b0a630a65ce2023-05-09T07:53:02ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752012-11-0120128911010.14232/ejqtde.2012.1.891807Asymptotic and oscillatory behavior of higher order quasilinear delay differential equationsBlanka Baculíková0Jozef Džurina1Technical University of Kosice, Kosice, SlovakiaTechnical University of Kosice, Kosice, SlovakiaIn the paper, we offer such generalization of a lemma due to Philos (and partially Staikos), that yields many applications in the oscillation theory. We present its disposal in the comparison theory and we establish new oscillation criteria for $n-$th order delay differential equation \begin{equation*} \left(r(t)\left[x'(t)\right]^{\gamma}\right)^{(n-1)}+q(t)x^{\gamma}(\tau(t))=0.\tag{$E$} \end{equation*} The presented technique essentially simplifies the examination of the higher order differential equations.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1807n-th order differential equationsoscillation |
| spellingShingle | Blanka Baculíková Jozef Džurina Asymptotic and oscillatory behavior of higher order quasilinear delay differential equations Electronic Journal of Qualitative Theory of Differential Equations n-th order differential equations oscillation |
| title | Asymptotic and oscillatory behavior of higher order quasilinear delay differential equations |
| title_full | Asymptotic and oscillatory behavior of higher order quasilinear delay differential equations |
| title_fullStr | Asymptotic and oscillatory behavior of higher order quasilinear delay differential equations |
| title_full_unstemmed | Asymptotic and oscillatory behavior of higher order quasilinear delay differential equations |
| title_short | Asymptotic and oscillatory behavior of higher order quasilinear delay differential equations |
| title_sort | asymptotic and oscillatory behavior of higher order quasilinear delay differential equations |
| topic | n-th order differential equations oscillation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1807 |
| work_keys_str_mv | AT blankabaculikova asymptoticandoscillatorybehaviorofhigherorderquasilineardelaydifferentialequations AT jozefdzurina asymptoticandoscillatorybehaviorofhigherorderquasilineardelaydifferentialequations |