# Bulletin of theKorean Mathematical SocietyBKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

## Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2022; 59(4): 827-841

Published online July 31, 2022 https://doi.org/10.4134/BKMS.b210490

## Uniqueness of meromorphic solutions of a certain type of difference equations

Jun-Fan Chen, Shu-Qing Lin

Fujian Normal University; Fujian Normal University

### Abstract

In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions $f(z)$ and $g(z)$ of the following complex difference equation $$A_{1}(z)f(z+1)+A_{0}(z)f(z)=F(z)e^{\alpha(z)}$$ when they share 0, $\infty$ CM, where $A_{1}(z),$ $A_{0}(z),$ $F(z)$ are non-zero polynomials, $\alpha(z)$ is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

Keywords: Difference equation, transcendental meromorphic solution, Nevanlinna theory, finite order

MSC numbers: 39B32, 30D35

Supported by: Project supported by the Natural Science Foundation of Fujian Province, China (Grant No. 2021J01651).

## Related articles in BKMS

• ### Entire solutions of differential-difference equations of Fermat type

2022; 59(1): 83-99

• ### On the existence of solutions of Fermat-type differential-difference equations

2021; 58(4): 983-1002

• ### Expressions of meromorphic solutions of a certain type of nonlinear complex differential equations

2020; 57(4): 1061-1073

• ### The generalized Fermat type difference equations

2018; 55(6): 1845-1858

more +