Meromorphic Solutions of Some Complex Difference Equations. (29th June 2009) - Huang, Zhi-Bo; Chen, Zong-Xuan
Abstract : The main purpose of this paper is to present the properties of the meromorphic solutions of complex difference equations of the form∑ J α J ( z ) ( ∏ j ∈ J f ( z + c j ) ) = R ( z, f ( z ) ), where J is a collection of all subsets of 1, 2, …, n , c j ( j ∈ J ) are distinct, nonzero complex numbers, f ( z ) is a transcendental meromorphic function, α J ( z ) 's are small functions relative tof ( z ), andR ( z, f ( z ) ) is a rational function inf ( z ) with coefficients which are small functions relative tof ( z ) .