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
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