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

Abstract

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