Copyright © 2009 Zhi-Bo Huang and Zong-Xuan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The main purpose of this paper is to present the properties of the meromorphic solutions of complex difference equations of the form ∑{J}αJ(z)(∏j∈Jf(z+cj))=R(z,f(z)), where {J} is a collection of all subsets of {1,2,…,n}, cj  (j∈J) are distinct, nonzero complex numbers, f(z) is a transcendental meromorphic function, αJ(z)'s are small functions relative to f(z), and R(z,f(z)) is a rational function in f(z) with coefficients which are small functions relative to f(z).