Chinese Quarterly Journal of Mathematics ›› 2019, Vol. 34 ›› Issue (3): 301-313.doi: 10.13371/j.cnki.chin.q.j.m.2019.03.008

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

  

  1. Institute of Applied Mathematics, South China Agricultural University
  • Received:2019-03-25 Online:2019-09-30 Published:2020-08-23
  • About author: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.
  • Supported by:
    supported by the National Natural Science Foundation of China(11701188)

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

CLC Number: