Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations

Abstract

Abstract:In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and nonhomogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.

Some Properties of Solutions for Someq-Difference Equations Containing Painlevé Equation

“…Journal of Function Spaces -difference operator of meromorphic functions, by utilizing the analog of Logarithmic Derivative Lemma on -difference operators given by Barnett et al [10]. Moreover, during the last decades, considerable attention has been paid to -difference operators, -difference equations, by replacing the -difference ( ), ∈ C \ {0, 1} with ( + ) of a meromorphic function in some complex difference equations and complex difference operators (see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]).…”

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

“…There are already some results on this topic (see e.g. [10,15]). As generalizations of Theorems 1-4, we obtain the following two results in the filed of complex linear differential-difference equations.…”