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Research Article | Open Access

Solutions to some generalized Fermat-type differential-difference equations

Zhiyong Xu, Junfeng Xu( )
School of Mathematics and Computational Sciences, Wuyi University, Jiangmen 529000, Guangdong, China
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Abstract

The main purpose of this article is to study Fermat-type complex differential-difference equations f(k)(z)2+[αf(z+c)−βf(z)]2=R(z). Our results improve some results due to Wang–Xu–Tu [AIMS. Mathematics, 2020], Zhang [Bull. Korean. Math. Soc, 2018], and Long–Qin [Applied Mathematics-A Journal of Chinese Universities, 2024]. Moreover, we provide some examples to show the existence of the solutions.

Keywords

meromorphic functionsFermat-type equationdifferential polynomialsNevanlinna theorydifferential-difference equation
CLC number: 30D35, 39A13, 39B72

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 34488-34503
DOI: 10.3934/math.20241643

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Cite this article:
Xu Z, Xu J. Solutions to some generalized Fermat-type differential-difference equations. AIMS Mathematics, 2024, 9(12): 34488-34503. https://doi.org/10.3934/math.20241643

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Received: 01 November 2024
Revised: 24 November 2024
Accepted: 29 November 2024
Published: 15 December 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)