@article{article_577219, title={Oscillation theorems for second-order nonlinear delay differential equations of neutral type}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={48}, pages={633–643}, year={2019}, author={Karpuz, Başak and Santra, Shyam S.}, keywords={Oscillation,nonoscillation,nonlinear,delay argument,second-order neutral differential equation}, abstract={In this paper, new sufficient conditions are obtained for oscillation of second-order neutral delay differential equations of the form <br />\[\frac{d}{dt}\bigg[r(t)\frac{d}{dt}[x(t)+p(t)x(\tau(t))]\bigg]+q(t)G\bigl(x(\sigma(t))\bigr)=0\: for\: t\geq t_{0},\] <br />under the assumptions $\int^{\infty}\frac{1}{r(\eta)}d\eta=\infty$ and $\int^{\infty}\frac{1}{r(\eta)}d\eta<\infty$ for various ranges of the bounded neutral coefficient $p$. Unlike most of the previous results, $\tau^{\prime}$ is allowed to be oscillatory. Further, some illustrative examples showing applicability of the new results are included. <br />}, number={3}, publisher={Hacettepe University}