Existence of zero-order meromorphic solutions of certain q-difference equations

In this paper, we consider the q -difference equation ( f ( q z ) + f ( z ) ) ( f ( z ) + f ( z / q ) ) = R ( z , f ) , where R ( z , f ) is rational in f and meromorphic in z . It shows that if the above equation assumes an admissible zero-order meromorphic solution f ( z ) , then either f ( z ) is...

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Bibliographic Details
Published in:Journal of inequalities and applications 2018, Vol.2018 (1), p.1-13, Article 217
Main Authors: Du, Yunfei, Gao, Zongsheng, Zhang, Jilong, Zhao, Ming
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Difference equations
Mathematics
Mathematics and Statistics
Meromorphic solution
Painlevé equations
q-Difference
Riccati equation
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Summary:In this paper, we consider the q -difference equation ( f ( q z ) + f ( z ) ) ( f ( z ) + f ( z / q ) ) = R ( z , f ) , where R ( z , f ) is rational in f and meromorphic in z . It shows that if the above equation assumes an admissible zero-order meromorphic solution f ( z ) , then either f ( z ) is a solution of a q -difference Riccati equation or the coefficients satisfy some conditions.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-018-1790-z