# PROPERTIES ON q-DIFFERENCE RICCATI EQUATION

• Huang, Zhi-Bo (School of Mathematical Sciences South China Normal University) ;
• Zhang, Ran-Ran (Department of Mathematics Guangdong University of Education)
• Accepted : 2018.03.16
• Published : 2018.11.30

#### Abstract

In this paper, we investigate a certain type of q-difference Riccati equation in the complex plane. We prove that q-difference Riccati equation possesses a one parameter family of meromorphic solutions if it has three distinct meromorphic solutions. Furthermore, we find that all meromorphic solutions of q-difference Riccati equation and corresponding second order linear q-difference equation can be expressed by q-gamma function if this q-difference Riccati equation admits two distinct rational solutions and $q{\in}{\mathbb{C}}$ such that 0 < ${\mid}q{\mid}$ < 1. The growth and value distribution of differences of meromorphic solutions of q-difference Riccati equation are also treated.

#### Acknowledgement

Supported by : Guangdong National Natural Science Foundation

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