Electron. J. Differential Equations, Vol. 2024 (2024), No. 26, pp. 1-21.

Entire solutions to Fermat-type difference and partial differential-difference equations in C^n

Hong Yan Xu, Goutam Haldar

Abstract:
In this article, we study the existence and the form of finite order transcendental entire solutions of systems of Fermat-type difference and partial differential-difference equations in several complex variables. Our results extend previous theorems given by Xu-Cao [49], Xu et al [52], and Zheng-Xu [55]. We give some examples to illustrate the content of this article.

Submitted January 6, 2024. Published March 25, 2024.
Math Subject Classifications: 39A45, 32H30, 30D35.
Key Words: Entire solutions; Fermat-type; partial differential equations; Nevanlinna theory.
DOI: 10.58997/ejde.2024.26

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Hong Yan Xu
School of Arts and Sciences
Suqian University
Suqian, Jiangsu 223800, China
email: xhyhhh@126.com
Goutam Haldar
Department of Mathematics
Ghani Khan Choudhury Institute of Engineering and Technology
Narayanpur, Malda - 732141, West Bengal, India
email: goutamiitm@gmail.com, goutamiit1986@gmail.com

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