On the Solution of Fermat-type Differential-di®erence Equations

LIU Dan, DENG Bing-mao, YANG De-gui

doi:10.13371/j.cnki.chin.q.j.m.2019.03.008

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 3: 301 - 313

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.03.008

On the Solution of Fermat-type Differential-di®erence Equations

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Institute of Applied Mathematics, South China Agricultural University

LIU Dan, Female, Guangdong, Associate Professor, Research area: Complex analysis, Uniqueness theory; DENG Bing-mao, Male, doctor, Research area: complex analysis; YANG De-gui, Male, Professor,Research area: Complex analysis, Complex Dynamics.

Received date: 2019-03-25

Online published: 2020-08-23

Supported by

supported by the National Natural Science Foundation of China(11701188)

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Abstract

In this paper,we mainly discuss entire solutions of finite order of the following Fermat type differential-difference equation[f^（k）（z）]²+[△_cf（z）]²=1,and the systems of differential-difference equations of the from. Our results can be proved to be the sufficient and necessary solutions to both equation and systems of equations.

Key words： Fermat-type equation; Differential-difference equation; Entire function

Cite this article

LIU Dan, DENG Bing-mao, YANG De-gui . On the Solution of Fermat-type Differential-di®erence Equations[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(3) : 301 -313 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.03.008

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