## Abstract and Applied Analysis

### Zeros, Poles, and Fixed Points of Meromorphic Solutions of Difference Painlevé Equations

#### Abstract

In this paper, we mainly study the properties of transcendental meromorphic solutions $f(z)$ of difference Painlevé equations $w(z+\mathrm{1})w(z-\mathrm{1})(w(z)-\mathrm{1})=\eta (z){w}^{\mathrm{2}}\mathrm{}(z)-\lambda (z)w(z)$ and $w(z+\mathrm{1})w(z-\mathrm{1})(w(z)-$ $\mathrm{1})=\eta (z)w(z)$ and obtain precise estimations of the exponents of convergence of zeros, poles of $\mathrm{\Delta }f(z)$ and $\mathrm{\Delta }f(z)/f(z)$, and of fixed points of $f(z+c)$ for any $c\in \Bbb C$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 782024, 8 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607229

Digital Object Identifier
doi:10.1155/2014/782024

Mathematical Reviews number (MathSciNet)
MR3198247

Zentralblatt MATH identifier
07023057

#### Citation

Lan, Shuang-Ting; Chen, Zong-Xuan. Zeros, Poles, and Fixed Points of Meromorphic Solutions of Difference Painlevé Equations. Abstr. Appl. Anal. 2014 (2014), Article ID 782024, 8 pages. doi:10.1155/2014/782024. https://projecteuclid.org/euclid.aaa/1412607229

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