Exact forms of entire solutions for Fermat type partial differential equations in C2

Abstract

This article studies the existence and the exact form of entire solutions of several Fermat type partial differential equations in C2, by utilizing the Nevanlinna theory of meromorphic functions in several complex variables. We obtain results about the existence and form of transcendental entire solutions with finite order for some variations of Fermat type functional equations. Our results are extensions and generalizations of the previous theorems by Xu and Cao [29,30], Liu and Dong [19].