NonExistence of Entire Solution of a Type of System of Equations 
Received:March 29, 2023 Revised:August 13, 2023 
Key Words:
transcendental entire function finite order system of differentialdifference equations

Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11971344). 

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Abstract: 
In this paper, we will prove that the system of differentialdifference equations \begin{eqnarray}\begin{cases}{(f(z)f'(z))}^n+p_1^2(z)g^m(z+\eta)=Q_1(z), \\\nonumber {(g(z)g'(z))}^n+p_2^2(z)f^m(z+\eta)=Q_2(z),\end{cases}\end{eqnarray} has no transcendental entire solution $(f(z),g(z))$ with $\rho(f,g)<\infty$ such that $\lambda(f)<\rho(f)$ and $\lambda(g)<\rho(g),$ where $P_1(z), Q_1(z), P_2(z)$ and $ Q_2(z)$ are nonvanishing polynomials. 
Citation: 
DOI:10.3770/j.issn:20952651.2024.02.008 
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