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

Abstract

The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equation [a(t) (x''(t)) α]'+q(t)x α(τ(t))=0, where 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. © 2011 Mathematical Institute, Slovak Academy of Sciences.