Research articles
ScienceAsia 49 (2023):ID 49-55 |doi:
10.2306/scienceasia1513-1874.2023.126
On existence of meromorphic solutions for certain
q-difference equation
Changwen Penga, Zongxuan Chenb, Huawei Huangc,*, Lei Taoc
ABSTRACT: We consider the existence of transcendental meromorphic solutions of q-difference equation
Xn
j=1
cj
(z)f (q
j
z) = P(z, f (z))
Q(z, f (z)),
where P(z, f (z)) and Q(z, f (z)) are polynomials in f having rational coefficients and no common roots, cj
(z) are
rational functions, q ? C and 0 < |q| ? 1. We obtain that such equation has no transcendental meromorphic solutions
for the case m = degf P ? degf Q ? 2.
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| a |
School of Mathematics and Information Science, Guiyang University, Guiyang 550005 China |
| b |
School of Mathematical Sciences, South China Normal University, Guangzhou 510631 China |
| c |
School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001 China |
* Corresponding author, E-mail: hwhuang7809@163.com
Received 10 Jan 2022, Accepted 7 Jun 2022
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