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 An(z)f(z+n)+⋯+A1(z)f(z+1)+A0(z)f(z)=0and =F(z), and for the linear difference polynomial g(z)=αn(z)f(z+n)+⋯+α1(z)f(z+1)+α0(z)f(z) generated by f(z), where Aj(z),αj(z) (j=0,1,…,n), F(z)(≢0) 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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