Meromorphic Solutions of Some Complex Difference Equations

The main purpose of this paper is to present the properties of the meromorphic solutions of complex difference equations of the form Sigma({J}) alpha(J)(Z)(Pi(j is an element of J)f(z + c(j))) = R(z, f(z)), where {J} is a collection of all subsets of {1, 2,..., n}, c(j) (j is an element of J) are distinct, nonzero complex numbers, f(z) is a transcendental meromorphic function, alpha(J)(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). Copyright (C) 2009 Z.-B. Huang and Z.-X. Chen.