Li, Tongxing; Zhang, Chenghui; Baculíková, Blanka; Džurina, Jozef On the oscillation of third-order quasi-linear delay differential equations. (English) Zbl 1265.34235 Tatra Mt. Math. Publ. 48, 117-123 (2011). The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equation \[ \biggl [a(t)\Bigl (x''(t)\Bigr)^{\alpha }\biggr ]'+q(t)x^{\alpha }\bigl (\tau (t)\bigr)=0\,, \tag{E} \] where \(\alpha >0\), \(\int _{t_0}^\infty {\frac {1}{a^{1/\alpha }(t)}\; {\operatorname {d}}t}<\infty \) and \(\tau (t)\leq t\). The authors 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. Reviewer: Božena Mihalíková (Košice) Cited in 6 Documents MSC: 34K11 Oscillation theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations Keywords:third-order delay differential equations; oscillation and asymptotic behavior Citations:Zbl 0954.34002 PDFBibTeX XMLCite \textit{T. Li} et al., Tatra Mt. Math. Publ. 48, 117--123 (2011; Zbl 1265.34235)