- Hacettepe Journal of Mathematics and Statistics
- Vol: 48 Issue: 3
- Oscillation theorems for second-order nonlinear delay differential equations of neutral type
Oscillation theorems for second-order nonlinear delay differential equations of neutral type
Authors : Başak Karpuz, Shyam S. Santra
Pages : 633-643
View : 15 | Download : 6
Publication Date : 2019-06-15
Article Type : Research
Abstract :In this paper, new sufficient conditions are obtained for oscillation of second-order neutral delay differential equations of the form \[\frac{d}{dt}\bigg[r(t)\frac{d}{dt}[x(t)+p(t)x(\tau(t))]\bigg]+q(t)G\bigl(x(\sigma(t))\bigr)=0\: for\: t\geq t_{0},\] 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.Keywords : Oscillation, nonoscillation, nonlinear, delay argument, second-order neutral differential equation