Oscillation theorems for second-order nonlinear delay differential equations of neutral type

Authors : Başak KARPUZ, Shyam S Santra

Pages : 633-643

View : 27 | Download : 7

Publication Date : 2019-06-15

Article Type : Research Paper

Abstract :In this paper, new sufficient conditions are obtained for oscillation of second-order neutral delay differential equations of the form \[\frac{d}{dt}\bigg[rinsert ignore into journalissuearticles values(t);\frac{d}{dt}[xinsert ignore into journalissuearticles values(t);+pinsert ignore into journalissuearticles values(t);xinsert ignore into journalissuearticles values(\tauinsert ignore into journalissuearticles values(t););]\bigg]+qinsert ignore into journalissuearticles values(t);G\biglinsert ignore into journalissuearticles values(xinsert ignore into journalissuearticles values(\sigmainsert ignore into journalissuearticles values(t););\bigr);=0\: for\: t\geq t_{0},\] under the assumptions $\int^{\infty}\frac{1}{rinsert ignore into journalissuearticles values(\eta);}d\eta=\infty$ and $\int^{\infty}\frac{1}{rinsert ignore into journalissuearticles values(\eta);}d\eta<\infty$ 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