Electron. J. Diff. Equ., Vol. 2014 (2014), No. 138, pp. 1-12.

Necessary and sufficient conditions for oscillation of neutral delay differential equations

Songbai Guo, Wanbiao Ma, B. G. Sampath Aruna Pradeep

Abstract:
In this article, we concerned with oscillation of the neutral delay differential equation $[x(t)-px(t-\tau)]'+qx(t-\sigma)=0$ with constant coefficients. By constructing several suitable auxiliary functions, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the aforementioned equation for the cases 0<p<1 and p>1.

Submitted March 17, 2014. Published June 16, 2014.
Math Subject Classifications: 34K06, 34K11, 34K40.
Key Words: Neutral delay differential equation; oscillation; characteristic equation

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Songbai Guo
Department of Applied Mathematics, School of Mathematics and Physics
University of Science and Technology Beijing
Beijing 100083, China
email: sonbguo@163.com
Wanbiao Ma
Department of Applied Mathematics, School of Mathematics and Physics
University of Science and Technology Beijing
Beijing 100083, China
email: wanbiao_ma@ustb.edu.cn
B. G. Sampath Aruna Pradeep
Department of Applied Mathematics, School of Mathematics and Physics
University of Science and Technology Beijing
Beijing 100083, China
email: sampath@maths.ruh.ac.lk

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