Electron. J. Differential Equations, Vol. 2023 (2023), No. 84, pp. 115.
Growth and value distribution of linear difference polynomials generated by meromorphic solutions of higherorder linear difference equations
Yi Xin Luo, Xiu Min Zheng
Abstract:
In this article, we investigate the relationship between growth and value
distribution of meromorphic solutions for the higherorder complex linear
difference equations
$$
A_n(z)f(z+n)+\dots+A_1(z)f(z+1)+A_0(z)f(z)=0 \quad \text{and } =F(z),
$$
and for the linear difference polynomial
$$
g(z)=\alpha_n(z)f(z+n)+\dots+\alpha_1(z)f(z+1)+\alpha_0(z)f(z)
$$
generated by \(f(z)\), where \(A_j(z),\alpha_j(z)\) (\(j=0,1,\dots,n\)),
\(F(z)(\not\equiv0)\) are meromorphic functions. We improve some previous
results due to Belaidi, Chen and Zheng and others.
Submitted May 24, 2023. Published December 16. 2023.
Math Subject Classifications: 30D35, 39A45.
Key Words: Linear difference equation; linear difference polynomial; meromorphic solution; growth; value distribution.
DOI: 10.58997/ejde.2023.84
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Yi Xin Luo
School of Mathematics and Statistics
Jiangxi Normal University
Nanchang, 330022, China
email: bellowinnie@163.com


Xiu Min Zheng
School of Mathematics and Statistics
Jiangxi Normal University
Nanchang, 330022, China
email: zhengxiumin2008@sina.com

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