Electron. J. Differential Equations, Vol. 2021 (2021), No. 18, pp. 1-11.

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

Yu Xian Chen, Hong Yan Xu

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].

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.

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Yu Xian Chen
School of Mathematics and computer science
Xinyu University, Xinyu, Jiangxi 338004, China
email: xygzcyx@126.com
Hong Yan Xu
School of Mathematics and computer science
Xinyu University
Xinyu, Jiangxi 338004, China
email: xhyhhh@126.com

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