English

Finite Logarithmic Order Meromorphic Solutions of Complex Linear Delay-Differential Equations

Complex Variables 2022-12-27 v1

Abstract

In this article, we study the growth of meromorphic solutions of linear delay-differential equation of the form \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), \end{equation*}% where Aij(z)A_{ij}(z) (i=0,1,,n,j=0,1,,m,n,mN)(i=0,1,\ldots ,n,j=0,1,\ldots ,m,n,m\in \mathbb{N}) and % F(z) are meromorphic of finite logarithmic order, ci(i=0,,n)c_{i}(i=0,\ldots ,n) are distinct non-zero complex constants. We extend those results obtained recently by Chen and Zheng, Bellaama and Bela\"{\i}di to the logarithmic lower order.

Keywords

Cite

@article{arxiv.2212.12825,
  title  = {Finite Logarithmic Order Meromorphic Solutions of Complex Linear Delay-Differential Equations},
  author = {Abdelkader Dahmani and Benharrat Belaïdi},
  journal= {arXiv preprint arXiv:2212.12825},
  year   = {2022}
}

Comments

23 pages

R2 v1 2026-06-28T07:52:00.305Z