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 |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 2414-3952 |