Electron. J. Diff. Equ., Vol. 2014 (2014), No. 73, pp. 1-14.

Oscillation of meromorphic solutions to linear differential equations with coefficients of [p,q]-order

Hong-Yan Xu, Jin Tu

Abstract:
We study the relationship between "small functions" and the derivative of solutions to the higher order linear differential equation
$$ f^{(k)}+A_{k-1}f^{(k-1)}+\dots+A_0f=0,\quad (k\geq 2) $$
Here $A_j(z)\; (j=0,1,\dots,k-1)$ are entire functions or meromorphic functions of [p,q]-order.

Submitted June 20, 2013. Published March 16, 2014.
Math Subject Classifications: 34M10, 30D35.
Key Words: Linear differential equation; oscillation; small function; [p,q]-order

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Hong-Yan Xu
Department of Informatics and Engineering
Jingdezhen Ceramic Institute
Jingdezhen, Jiangxi 333403, China
email: xhyhhh@126.com
Jin Tu
Institute of Mathematics and informatics
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: tujin2008@sina.com

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