Electron. J. Differential Equations, Vol. 2017 (2017), No. 34, pp. 1-15.

Growth of meromorphic solutions to homogeneous and non-homogeneous linear (differential-)difference equations with meromorphic coefficients

Yan-Ping Zhou, Xiu-Min Zheng

Abstract:
In this article, we study the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations and linear differential-difference equations. When there exists only one coefficient having the maximal iterated order or having the maximal iterated type among those having the maximal iterated order, and the above coefficient satisfies certain conditions on its poles, we obtain estimates on the lower bound of the iterated order of the meromorphic solutions. The case p=1 is also discussed and corresponding results are obtained by strengthening some conditions.

Submitted August 22, 2016. Published January 30, 2017.
Math Subject Classifications: 30D35, 39B32, 39A10.
Key Words: Linear difference equation; linear differential-difference equation; meromorphic solution; iterated order; iterated type.

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Yan-Ping Zhou
Institute of Mathematics and Information Science
Jiangxi Normal University
Nanchang 330022, China
email: m18720964375@163.com
Xiu-Min Zheng
Institute of Mathematics and Information Science
Jiangxi Normal University
Nanchang 330022, China
email: zhengxiumin2008@sina.com

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