Electron. J. Differential Equations, Vol. 2023 (2023), No. 84, pp. 1-15.

Growth and value distribution of linear difference polynomials generated by meromorphic solutions of higher-order 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 higher-order 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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