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http://dx.doi.org/10.4134/BKMS.b171049

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.6, 2018 , pp. 1755-1771 More about this Journal
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.
Keywords
q-difference Riccati equation; q-difference equation; q-gamma function;
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