ON THE OSCILLATION OF A THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NEUTRAL TYPE
In this article, we investigate that oscillation behavior of the solutions of the third-order nonlinear differential equation with neural type of the form $$ \Big(a_{1}(t)\big(a_{2}(t)Z^{\prime}(t)\big)^{\prime}\Big)^{\prime} + q(t) f\big(x(\sigma(t))\big) = 0, \quad t\geq t_0 > 0, $$ where \(Z(t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2017-12-01
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| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/90 |
| _version_ | 1828221339695054848 |
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| author | V. Ganesan Marappan Sathish Kumar |
| author_facet | V. Ganesan Marappan Sathish Kumar |
| author_sort | V. Ganesan |
| collection | DOAJ |
| description | In this article, we investigate that oscillation behavior of the solutions of the third-order nonlinear differential equation with neural type of the form
$$
\Big(a_{1}(t)\big(a_{2}(t)Z^{\prime}(t)\big)^{\prime}\Big)^{\prime}
+ q(t) f\big(x(\sigma(t))\big) = 0, \quad t\geq t_0 > 0,
$$
where \(Z(t) := x(t)+p(t)x^{\alpha}(\tau(t))\). Some new oscillation results are presented that extend those results given in the literature. |
| first_indexed | 2024-04-12T16:39:02Z |
| format | Article |
| id | doaj.art-f91227960760482d8d44e7c46920d5b5 |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-04-12T16:39:02Z |
| publishDate | 2017-12-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-f91227960760482d8d44e7c46920d5b52022-12-22T03:24:52ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522017-12-013210.15826/umj.2017.2.01339ON THE OSCILLATION OF A THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NEUTRAL TYPEV. Ganesan0Marappan Sathish Kumar1Aringar Anna Government Arts College, Namakkal, TamilnaduPaavai Engineering College, Pachal, Namakkal, TamilnaduIn this article, we investigate that oscillation behavior of the solutions of the third-order nonlinear differential equation with neural type of the form $$ \Big(a_{1}(t)\big(a_{2}(t)Z^{\prime}(t)\big)^{\prime}\Big)^{\prime} + q(t) f\big(x(\sigma(t))\big) = 0, \quad t\geq t_0 > 0, $$ where \(Z(t) := x(t)+p(t)x^{\alpha}(\tau(t))\). Some new oscillation results are presented that extend those results given in the literature.https://umjuran.ru/index.php/umj/article/view/90Oscillation, Non-linear, Neutral differential equation, Third order. |
| spellingShingle | V. Ganesan Marappan Sathish Kumar ON THE OSCILLATION OF A THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NEUTRAL TYPE Ural Mathematical Journal Oscillation, Non-linear, Neutral differential equation, Third order. |
| title | ON THE OSCILLATION OF A THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NEUTRAL TYPE |
| title_full | ON THE OSCILLATION OF A THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NEUTRAL TYPE |
| title_fullStr | ON THE OSCILLATION OF A THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NEUTRAL TYPE |
| title_full_unstemmed | ON THE OSCILLATION OF A THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NEUTRAL TYPE |
| title_short | ON THE OSCILLATION OF A THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NEUTRAL TYPE |
| title_sort | on the oscillation of a third order nonlinear differential equations with neutral type |
| topic | Oscillation, Non-linear, Neutral differential equation, Third order. |
| url | https://umjuran.ru/index.php/umj/article/view/90 |
| work_keys_str_mv | AT vganesan ontheoscillationofathirdordernonlineardifferentialequationswithneutraltype AT marappansathishkumar ontheoscillationofathirdordernonlineardifferentialequationswithneutraltype |