Meromorphic Solutions of Some Complex Difference Equations

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).