Uniqueness of Meromorphic Solutions for a Class of Complex Linear DifferentialDifference Equations 
Received:April 02, 2021 Revised:January 11, 2022 
Key Words:
meromorphic solution complex differentialdifference equation shared value uniqueness finite order

Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12001211) and the Natural Science Foundation of Fujian Province, China (Grant No.2021J01651). 

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Abstract: 
In this paper, we mainly study the uniqueness of transcendental meromorphic solutions for a class of complex linear differentialdifference equations. Specially, suppose that $f(z)$ is a finite order transcendental meromorphic solution of complex linear differentialdifference equation: $W_{1}(z)f'(z+1)+W_{2}(z)f(z)=W_{3}(z)$, where $W_{1}(z)$, $W_{2}(z)$, $W_{3}(z)$ are nonzero meromorphic functions, with their orders of growth being less than one, such that $W_{1}(z)+W_{2}(z)\not\equiv0$. If $f(z)$ and a meromorphic function $g(z)$ share 0, 1, $\infty$ CM, then either $f(z)\equiv g(z)$ or $f(z)+g(z)\equiv f(z)g(z)$ or $f^{2}(z)(g(z)1)^{2}+g^{2}(z)(f(z)1)^{2}\equiv f(z)g(z)(f(z)g(z)1)$ or there exists a polynomial $\varphi(z)=az+b_{0}$ such that $f(z)=\frac{1e^{\varphi(z)}}{e^{\varphi(z)}(e^{a_{0}b_{0}}1)}$, $g(z)=\frac{1e^{\varphi(z)}}{1e^{b_{0}a_{0}}}$, where $a\,(\neq 0)$, $a_{0}$, $b_{0}$ are constants with $e^{a_{0}}\neq e^{b_{0}}$. 
Citation: 
DOI:10.3770/j.issn:20952651.2022.04.001 
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