Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 18, pp. 1-11.

Title: Exact forms of entire solutions for Fermat type partial differential equations in C^2
       
Authors: Yu Xian Chen (Xinyu Univ., Xinyu, Jiangxi, China)
         Hong Yan Xu (Xinyu Univ., Xinyu, Jiangxi, China)

Abstract:
 This article studies the existence and the exact form of entire
 solutions of several Fermat type partial differential equations in $\mathbb{C}^2$,
 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].

Submitted January 7, 2021. Published March 24, 2021.
Math Subject Classifications: 30D35, 35M30, 32W50, 39A45.
Key Words: Fermat type; Nevanlinna theory; existence; entire solution;
           complex partial differential equation.