Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 84, pp. 1-15.

Title: Growth and value distribution of linear difference polynomials generated by meromorphic solutions  of higher-order linear difference equations
       
Authors: Yi Xin Luo (Jiangxi Normal Univ., Nanchang, China)
         Xiu Min Zheng (Jiangxi Normal Univ., Nanchang, China)

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.