Electron. J. Differential Equations, Vol. 2018 (2018), No. 159, pp. 1-15.

Oscillation of second-order Emden-Fowler neutral delay differential equations

Yingzhu Wu, Yuanhong Yu, Jinsen Xiao

Abstract:
In this article, we establish new oscillation criteria for the second-order Emden-Fowler neutral delay differential equation
$$ \Big(r(t)|z'(t)|^{\alpha-1}z'(t)\Big)'+q(t)|x(\sigma(t))|^{\beta-1} x\big(\sigma(t)\big)=0, $$
where $z(t)=x(t)+p(t)x(\tau(t)), \alpha>0$ and $\beta>0$. Our results improve some well-known results which were published recently in the literature. Some illustrative examples are also provided to show the significance of our results.

Submitted August 6, 2017. Published September 4, 2018.
Math Subject Classifications: 34C10, 34K11
Key Words: Emden-Fowler equation; half-linear differential equation; Riccati method; oscillation criterion.

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Yingzhu Wu
Department of Mathematics
Guangdong University of Petrochemical Technology
Maoming 525000, China
email: yingzhu1978@163.com
Yuanhong Yu
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing 100190, China
email: yu84845366@126.com
Jinsen Xiao
School of Sciences
Guangdong University of Petrochemical Technology
Maoming 525000, China
email: jinsenxiao@yahoo.com

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