Bulletin of the
Korean Mathematical Society
BKMS

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

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

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

Copyright © The Korean Mathematical Society.

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).