Non-Existence 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 differential-difference equations  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11971344).
Author NameAffiliation
Zhiwei ZHOU School of Mathematics, Suzhou University of Science and Technology, Jiangsu 215009, P. R. China 
Ying ZHANG Information Construction and Management Center, Suzhou University of Science and Technology, Jiangsu 215009, P. R. China 
Zhigang HUANG School of Mathematics, Suzhou University of Science and Technology, Jiangsu 215009, P. R. China 
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Abstract:
      In this paper, we will prove that the system of differential-difference 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 non-vanishing polynomials.
Citation:
DOI:10.3770/j.issn:2095-2651.2024.02.008
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