$\wp$-函数," /> $\wp$-函数,"/> $\wp$-functions,"/> Meromorphic Solutions of Finite Order to the Equation <inline-formula><tex-math id="M2">$f^{n}+f^{m}(z+c)=e^{Az+B}$</tex-math></inline-formula>

Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 913-920.

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Meromorphic Solutions of Finite Order to the Equation $f^{n}+f^{m}(z+c)=e^{Az+B}$

Minfeng Chen1,*(),Zongsheng Gao2,Zhibo Huang3   

  1. 1 School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006
    2 LMIB & School of Mathematical Sciences, Beihang University, Beijing 100191
    3 School of Mathematical Sciences, South China Normal University, Guangzhou 510631
  • Received:2020-10-28 Online:2021-08-26 Published:2021-08-09
  • Contact: Minfeng Chen E-mail:chenminfeng198710@126.com
  • Supported by:
    the NSFC(12001117);the NSFC(12001503);the NSFC(11701524);the NSF of Guangdong Province(2018A030313267);the NSF of Guangdong Province(2018A030313508)


In this paper, we study the meromorphic solutions of finite order to the difference equations $f^{n}(z)+f^{m}(z+c)=e^{Az+B}$ $(c\neq 0)$ over the complex plane ${\mathbb C}$ for integers $n, m$, and $A, B, c\in {\mathbb C}$.

Key words: Fermat-type difference equations, Meromorphic solution, Nevanlinna theory, $\wp$-functions')">Weierstrass's $\wp$-functions

CLC Number: 

  • O175.29