Meromorphic solutions of higher order non-homogeneous linear difference equations

Abstract

In this paper, we investigate the growth of meromorphic solutions of nonhomogeneous linear difference equation A_n(z)f(z + c_n) + · · · + A_1(z)f(z + c_1) + A_0(z)f(z) = A_{n+1}(z), where A_{n+1 (z), · · · , A0 (z) are (entire) or meromorphic functions and c_j (1, · · · , n) are non-zero distinct complex numbers. Under some conditions on the (lower) order and the (lower) type of the coefficients, we obtain estimates on the lower bound of the order of meromorphic solutions of the above equation. We extend early results due to Luo and Zheng.