On Transcendental Entire Solutions of System of Non-Linear Complex Differential-Difference Equations

Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of transcendental entire solutions of one type of system of complex differential-difference equations, and provide the explicit form of all transcendental entire function solutions to the system of equations, as well as several existence conditions for the system. In fact, we consider a broader class of system, which contains the corresponding system for equation studied in the reference Scientia Sinica Mathematica 2019, 49 by Liu and Gao. These findings extend the existing results of complex differential (difference) equations to the systems of differential-difference equations.