The aim of this work is to study asymptotic properties of thethird-order quasi-linear delay differential equation\begin{equation*}\label{E}\left[a(t)\left(x''(t)\right)^\alpha\right]'+q(t)x^\alpha(\tau(t))=0, \tag{$E$}\end{equation*}%where $\alpha>0$, $\int_{t_0}^\infty\frac{1}{a^{1/\alpha}(t)}{\rmd}t<\infty$ and $\tau(t)\leq t$. We establish a new condition which guarantees that every solution of $(E)$ is either oscillatory or converges to zero. These results improve some known results in the literature. An example is given to illustrate the main results.
@article{107,
title = {On the oscillation of third-order quasi-linear delay differential equations},
journal = {Tatra Mountains Mathematical Publications},
volume = {49},
year = {2011},
doi = {10.2478/tatra.v48i0.107},
language = {EN},
url = {http://dml.mathdoc.fr/item/107}
}
Li, Tongxing; Zhang, Chenghui; Baculíková, Blanka; Džurina, Jozef. On the oscillation of third-order quasi-linear delay differential equations. Tatra Mountains Mathematical Publications, Tome 49 (2011) . doi : 10.2478/tatra.v48i0.107. http://gdmltest.u-ga.fr/item/107/