Oscillation of second order neutral delay differential equations

Abstract

We establish some new oscillation criteria for the second order neutral delay differential equation $$ [r(t)|[x(t)+p(t)x[\tau (t)]]'|^{\alpha -1} [x(t)+ p(t)x[\tau (t)]]']' +\,q(t)f(x[\sigma (t)])=0. $$ The obtained results supplement those of Dzurina and Stavroulakis, Sun and Meng, Xu and Meng, Baculíková and Lacková. We also make a slight improvement of one assumption in the paper of Xu and Meng.