Entire Solutions of the Systems of Complex Differential-Difference Equations

TL;DR

This paper investigates the existence and properties of entire solutions of complex differential-difference equations of Fermat type using Nevanlinna theory, extending previous results in the field.

Contribution

It extends Liu and Gao's results by establishing conditions for finite order entire solutions of systems of complex differential-difference equations.

Findings

Existence of finite order entire solutions is established.

Results extend previous work by Liu and Gao.

Uses Nevanlinna's value distribution and difference theory.

Abstract

Using Nevanlinna's value distribution theory and the complex difference theory , the existence of the finite order of the entire solutions of the Fermat type of the complex differential-difference equation and the systems of complex differential-difference equations are investigated, and obtained some results, which extends Liu and Gao's results.