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December 2021 Transcendental entire solutions of several Fermat type PDEs and PDDEs with two complex variables
Hong Yan Xu, Jin Tu, Hua Wang
Rocky Mountain J. Math. 51(6): 2217-2235 (December 2021). DOI: 10.1216/rmj.2021.51.2217

Abstract

This article is concerned with the description of transcendental entire solutions of several Fermat type functional equations in 2 concerning partial differential-difference equations and partial differential equations. By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we establish some results about the existence and the forms of entire solutions for such equations, which are some improvements and generalizations of the previous theorems. Moreover, some examples are given illustrating that our results are precise to some extent.

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Hong Yan Xu. Jin Tu. Hua Wang. "Transcendental entire solutions of several Fermat type PDEs and PDDEs with two complex variables." Rocky Mountain J. Math. 51 (6) 2217 - 2235, December 2021. https://doi.org/10.1216/rmj.2021.51.2217

Information

Received: 17 November 2020; Revised: 21 March 2021; Accepted: 22 March 2021; Published: December 2021
First available in Project Euclid: 22 March 2022

Digital Object Identifier: 10.1216/rmj.2021.51.2217

Subjects:
Primary: 30D35 , 32W50 , 35M30 , 39A45

Keywords: entire function , existence , Fermat equation , partial differential-difference equation

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 6 • December 2021
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