Electron. J. Diff. Equ., Vol. 2015 (2015), No. 199, pp. 1-11.

Properties of Schwarzian difference equations

Shuang-Ting Lan, Zong-Xuan Chen

Abstract:
We consider the Schwarzian type difference equation
$$ \Big[\frac{\Delta^{3}f(z)}{\Delta f(z)}-\frac{3}{2} \Big(\frac{\Delta^{2}f(z)}{\Delta f(z)}\Big)^{2}\Big]^{k}=R(z), $$
where R(z) is a nonconstant rational function. We study the existence of rational solutions and value distribution of transcendental meromorphic solutions with finite order of the above equation.

Submitted April 22, 2015. Published August 4, 2015.
Math Subject Classifications: 30D35, 34A20.
Key Words: Schwarzian difference equation; rational solution; value distribution.

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Shuang-Ting Lan
Department of Mathematics
Guangzhou Civil Aviation College
Guangzhou 510403, China
email: wqh200811@126.com
Zong-Xuan Chen
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: chzx@vip.sina.com

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