Properties on $q$-difference Riccati equation

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 solu...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2018, 55(6), , pp.1755-1771
Main Authors: Zhibo Huang, Ran-Ran Zhang
Format: Article
Language:English
Subjects:
수학
Online Access:Get full text
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Summary: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
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.b171049