Geodesic
On the oscillation of third-order quasi-linear neutral functional differential equations
Archivum mathematicum, Tome 47 (2011) no. 3, pp. 181-199 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation \begin{equation*} \big [a(t)\big ([x(t)+p(t)x(\delta (t))]^{\prime \prime }\big )^\alpha \big ]^{\prime }+q(t)x^\alpha (\tau (t))=0\,, E \end{equation*} where $\alpha >0$, $0\le p(t)\le p_0\infty $ and $\delta (t)\le t$. By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results.
The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation \begin{equation*} \big [a(t)\big ([x(t)+p(t)x(\delta (t))]^{\prime \prime }\big )^\alpha \big ]^{\prime }+q(t)x^\alpha (\tau (t))=0\,, E \end{equation*} where $\alpha >0$, $0\le p(t)\le p_0\infty $ and $\delta (t)\le t$. By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results.
Classification : 34C10, 34K11
Keywords: third-order; neutral functional differential equations; oscillation and asymptotic behavior 
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Thandapani, E.; Li, Tongxing. On the oscillation of third-order quasi-linear neutral functional differential equations. Archivum mathematicum, Tome 47 (2011) no. 3, pp. 181-199. http://geodesic.mathdoc.fr/item/ARM_2011_47_3_a1/

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