Oscillation criteria for even order nonlinear neutral differential equations
In this paper, we consider the oscillation criteria for even order nonlinear neutral differential equations of the form $$ \left(r(t)z^{(n-1)}(t)\right)'+q(t)f(x(\sigma(t)))=0, $$ where $z(t)=x(t)+p(t)x(\tau(t)),$ $n\geq2$ is a even integer. The results are obtained both for the case $\int^\inf...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2012-04-01
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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=1275 |
| _version_ | 1827951287046504448 |
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| author | Yibing Sun Zhenlai Han Shurong Sun Chao Zhang |
| author_facet | Yibing Sun Zhenlai Han Shurong Sun Chao Zhang |
| author_sort | Yibing Sun |
| collection | DOAJ |
| description | In this paper, we consider the oscillation criteria for even order nonlinear neutral differential equations of the form
$$
\left(r(t)z^{(n-1)}(t)\right)'+q(t)f(x(\sigma(t)))=0,
$$
where $z(t)=x(t)+p(t)x(\tau(t)),$ $n\geq2$ is a even integer. The results are obtained both for the case $\int^\infty r^{-1}(t){\rm d}t=\infty,$ and in case $\int^\infty r^{-1}(t){\rm d}t<\infty.$ These criteria here derived extend and improve some known results in literatures. Some examples are given to illustrate our main results. |
| first_indexed | 2024-04-09T13:40:32Z |
| format | Article |
| id | doaj.art-69552bd5fcaa437487be80455dd21970 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:40:32Z |
| publishDate | 2012-04-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-69552bd5fcaa437487be80455dd219702023-05-09T07:53:02ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752012-04-0120123011210.14232/ejqtde.2012.1.301275Oscillation criteria for even order nonlinear neutral differential equationsYibing Sun0Zhenlai Han1Shurong Sun2Chao Zhang3University of Jinan, Jinan, Shandong, P. R. ChinaUniversity of Jinan, Jinan, Shandong, P. R. ChinaUniversity of Jinan, Jinan, Shandong, P. R. ChinaUniversity of Jinan, Jinan, Shandong, P. R. ChinaIn this paper, we consider the oscillation criteria for even order nonlinear neutral differential equations of the form $$ \left(r(t)z^{(n-1)}(t)\right)'+q(t)f(x(\sigma(t)))=0, $$ where $z(t)=x(t)+p(t)x(\tau(t)),$ $n\geq2$ is a even integer. The results are obtained both for the case $\int^\infty r^{-1}(t){\rm d}t=\infty,$ and in case $\int^\infty r^{-1}(t){\rm d}t<\infty.$ These criteria here derived extend and improve some known results in literatures. Some examples are given to illustrate our main results.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1275oscillationeven ordernonlinear neutral differential equations |
| spellingShingle | Yibing Sun Zhenlai Han Shurong Sun Chao Zhang Oscillation criteria for even order nonlinear neutral differential equations Electronic Journal of Qualitative Theory of Differential Equations oscillation even order nonlinear neutral differential equations |
| title | Oscillation criteria for even order nonlinear neutral differential equations |
| title_full | Oscillation criteria for even order nonlinear neutral differential equations |
| title_fullStr | Oscillation criteria for even order nonlinear neutral differential equations |
| title_full_unstemmed | Oscillation criteria for even order nonlinear neutral differential equations |
| title_short | Oscillation criteria for even order nonlinear neutral differential equations |
| title_sort | oscillation criteria for even order nonlinear neutral differential equations |
| topic | oscillation even order nonlinear neutral differential equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1275 |
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