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

Abstract

In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous 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.

Keywords

• complex linear differential-difference equation
• meromorphic solution
• small function
• order
• convergence exponent
• 30d35
• 39b32
• 39a10