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Research articles

ScienceAsia 49 (2023): 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