$f^{n}(z)+f^{m}(z+c)=e^{Az+B}$的有限级亚纯解

数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 913-920.

• 论文 • 下一篇

$f^{n}(z)+f^{m}(z+c)=e^{Az+B}$的有限级亚纯解

陈敏风^1,*(),高宗升²,黄志波³

¹ 广东外语外贸大学数学与统计学院广州 510006
² 北京航空航天大学LMIB& 数学科学学院北京 100191
³ 华南师范大学数学科学学院广州 510631

收稿日期:2020-10-28 出版日期:2021-08-26 发布日期:2021-08-09
通讯作者: 陈敏风 E-mail:chenminfeng198710@126.com
基金资助:
国家自然科学基金(12001117);国家自然科学基金(12001503);国家自然科学基金(11701524);广东省自然科学基金(2018A030313267);广东省自然科学基金(2018A030313508)

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

Minfeng Chen^1,*(),Zongsheng Gao²,Zhibo Huang³

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)

摘要/Abstract

摘要：

该文研究了复平面上的差分方程$f^{n}（z）+f^{m}（z+c）=e^{Az+B}$$（c\neq 0）$的有限级亚纯解，其中$n，m$为整数，$A，B，c\in{\mathbb C}$为复数.

关键词: 费马型差分方程, 亚纯解, 奈望林纳理论, $\wp$-函数')">魏尔斯特拉斯$\wp$-函数

Abstract:

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

中图分类号:

O175.29

陈敏风,高宗升,黄志波. $f^{n}(z)+f^{m}(z+c)=e^{Az+B}$的有限级亚纯解[J]. 数学物理学报, 2021, 41(4): 913-920.

Minfeng Chen,Zongsheng Gao,Zhibo Huang. Meromorphic Solutions of Finite Order to the Equation $f^{n}+f^{m}(z+c)=e^{Az+B}$[J]. Acta mathematica scientia,Series A, 2021, 41(4): 913-920.

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$f^{n}(z)+f^{m}(z+c)=e^{Az+B}$的有限级亚纯解

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

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