Growth of Meromorphic Solutions of General Complex Linear Differential-Difference Equation

Abstract

In this paper, we investigate the ralations between the growth of entire or meromorphic coefficients and the growth of meromorphic solutions of general complex linear differential-difference equation, and obtain the lower bound of the order of meromorphic solutions by comparing the (lower) orders or the (lower) types of the coefficients. Our results can be seen as generalizations for both the case of complex linear differential equation and the case of complex linear difference equation.

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

“…Since then, many authors used them in order to generalize previous results obtained on the growth of solutions of linear difference equations and linear differential equations in which the coefficients are entire or meromorphic functions in the complex plane C of positive order different to zero, see for example [1,6,11,14,19,21,22], their new results were on the logarithmic order, the logarithmic lower order and the logarithmic exponent of convergence, where they considered the case when the coefficients are of zero order see, for example, [2-4, 7, 12, 17, 18, 23]. In this article, we also use these concepts to investigate the lower logarithmic order of solutions to more general homogeneous and non homogeneous linear delay-differential equations, where we generalize those results obtained in [5,8]. We start by stating some important definitions.…”

“…Recently, the research on the properties of meromorphic solutions of complex delay-differential equations has become a subject of great interest from the viewpoint of Nevanlinna theory and its difference analogues. In [20], Liu, Laine and Yang presented developments and new results on complex delay-differential equations, an area with important and interesting applications, which also gathers increasing attention (see, [4,5,8,24]. In [8], Chen and Zheng considered the following homogeneous complex delay-differential equation…”

“…In [20], Liu, Laine and Yang presented developments and new results on complex delay-differential equations, an area with important and interesting applications, which also gathers increasing attention (see, [4,5,8,24]. In [8], Chen and Zheng considered the following homogeneous complex delay-differential equation…”