On the entire solutions for several partial differential difference equations (systems) of Fermat type in C²

Abstract

By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we will establish some theorems about the existence and the forms of entire solutions for several partial differential difference equations (systems) of Fermat type with two complex variables such as andwhich are some extensions and generalizations of the previous theorems given by Xu and Cao [29,30], Xu, Liu and Li [28], and Liu, Yang [18,19,20]. Moreover, we give some examples to explain that our results are precise to some extent.

Keywords

• nevanlinna theory
• entire function
• partial differential difference equation system