We consider the Schwarzian type difference equation
![$$
\Big[\frac{\Delta^{3}f(z)}{\Delta f(z)}-\frac{3}{2}
\Big(\frac{\Delta^{2}f(z)}{\Delta f(z)}\Big)^{2}\Big]^{k}=R(z),
$$](gifs/aa.gif)
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.
Shuang-Ting Lan, Zong-Xuan Chen
Abstract:
We consider the Schwarzian type difference equation
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 |
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Zong-Xuan Chen School of Mathematical Sciences South China Normal University Guangzhou 510631, China email: chzx@vip.sina.com |
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