Meromorphic solutions of a type of system of complex differential-difference equations

Abstract

Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form (*){∑j=1nαj(z)f1(λj1)(z+cj)=R2(z,f2(z)),∑j=1nβj(z)f2λj2(z+cj)=R1(z,f1(z)). where λij (j = 1,2,···, n; i = 1,2) are finite non-negative integers, and cj (j = 1,2,·,n) are distinct, nonzero complex numbers, αj(z), βj(z) (j = 1,2,·,n) are small functions relative to fi(z) (i = 1,2) respectively, Ri(z,f(z)) (i = 1,2) are rational in fi(z) (i = 1,2) with coefficients which are small functions of fi(z)(i = 1,2) respectively.