On the oscillation of third-order quasi-linear delay differential equations

Year, pages: 2011, 117 - 123

The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equation

\begin{equation*}\label{E} [a(t)(x''(t))^α]^\prime+q(t)x^α(τ(t)\br)=0, \tag{$E$} \end{equation*}

where $α>0$, $\int_t0^∞((1) / (a^1/α(t))){ d}t<∞$ and $τ(t)≤ t$. 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

Li, T., Zhang, C., Baculíková, B., Džurina, J. 2011. On the oscillation of third-order quasi-linear delay differential equations. In Tatra Mountains Mathematical Publications, vol. 48, no.1, pp. 117-123. 1210-3195.

Li, T., Zhang, C., Baculíková, B., Džurina, J. (2011). On the oscillation of third-order quasi-linear delay differential equations. Tatra Mountains Mathematical Publications, 48(1), 117-123. 1210-3195.