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Research articles

ScienceAsia 49 (2023): 369-376 |doi: 10.2306/scienceasia1513-1874.2023.002

On existence of meromorphic solutions for nonlinear q-difference equation

Changwen Penga,*, Huawei Huangb, Lei Taob,c

ABSTRACT:     : In this paper, we mainly consider the existence of meromorphic solutions of nonlinear q-difference equation of type f (qz) + f (z/q) = P(z, f (z)) Q(z, f (z)), where the right-hand side is irreducible, P(z, f (z)) and Q(z, f (z)) are polynomials in f with rational coefficients, and q is a nonzero complex constant. We obtain that such equation has no transcendental meromorphic solution when |q| = 1 and m = degf (P)?degf (Q) > 1. And we investigate the growth of transcendental meromorphic solutions of nonlinear q-difference equation and find lower bounds for their characteristic functions for transcendental meromorphic solutions of such equation for the case |q| ?= 1.

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a College of Mathematics and Information Science, Guiyang University, Guiyang 550005 China
b School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001 China
c School of Mathematics and Big Data, Guizhou Education University, Guiyang 550018 China

* Corresponding author, E-mail: pengcw716@126.com

Received 12 Apr 2022, Accepted 2 Sep 2022