$f^{n}(z)+f^{m}(z+c)=e^{Az+B}$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.

参考文献 22

1	Baker I N . On a class of meromorphic functions. Proc Amer Math Soc, 1966, 17 (4): 819- 822 doi: 10.1090/S0002-9939-1966-0197732-X
2	Bank S B , Langley J K . On the value distribution theory of elliptic functions. Monatsh Math, 1984, 98, 1- 20 doi: 10.1007/BF01536904
3	Bergweiler W . Order and lower order of composite meromorphic functions. Michigan Math J, 1989, 36 (1): 135- 146
4	Chen W , Han Q , Liu J B . On Fermat Diophantine functional equations, little Picard theorem and beyond. Aequat Math, 2019, 93 (2): 425- 432 doi: 10.1007/s00010-018-0614-z
5	Chiang Y M , Feng S J . On the Nevanlinna characteristic of $f(z+\eta)$ and difference equations in the complex plane. Ramanujan J, 2008, 16 (1): 105- 129 doi: 10.1007/s11139-007-9101-1
6	Edrei A , Fuchs W H J . On the zeros of $f(g(z))$ where $f$ and $g$ are entire functions. J Anal Math, 1964, 12, 243- 255 doi: 10.1007/BF02807435
7	Gross F . On the equation $f^{n}+g^{n}=1.$ Ⅰ. Bull Amer Math Soc, 1966, 72, 86- 88 doi: 10.1090/S0002-9904-1966-11429-5
8	Gross F . On the equation $f^{n}+g^{n}=1.$ Ⅱ. Bull Amer Math Soc, 1968, 74, 647- 648 doi: 10.1090/S0002-9904-1968-11975-5
9	Hayman W K . Meromorphic Function. Oxford: Clarendon Press, 1964
10	Halburd R G , Korhonen R J . Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. J Math Anal Appl, 2006, 314, 477- 487 doi: 10.1016/j.jmaa.2005.04.010
11	Han Q , Lü F . On the equation $f^{n}(z)+g^{n}(z)=e^{\alpha z+\beta}$ . J Contemp Math Anal, 2019, 54 (2): 98- 102 doi: 10.3103/S1068362319020067
12	Huber A . A novel class of solutions for a nonlinear third order wave equation generated by the Weierstra $\beta$ transformation. Chaos Solitons & Fractals, 2006, 28 (4): 972- 978
13	Jategaonkar A V . Elementary proof of a theorem of P. Montel on entire functions. J Lond Math Soc, 1965, 40, 166- 170
14	Laine I . Nevanlinna Theory and Complex Differential Equations. Berlin: De Gruyter, 1993
15	Li B Q . On meromorphic solutions of $f^{2}+g^{2}=1$ . Math Z, 2008, 258, 763- 771 doi: 10.1007/s00209-007-0196-2
16	Li B Q , Ye Z . On meromorphic solutions of $f^{3}+g^{3}=1$ . Arch Math, 2008, 90, 39- 43 doi: 10.1007/s00013-007-2371-4
17	Li B Q. On Fermat-type Functional and Partial Differential Equations//Sabadini I, Struppa D, et al. The Mathematical Legacy of Leon Ehrenpreis. Milano: Springer, 2012: 209-222
18	Lü F , Han Q . On the Fermat-type equation $f^{3}(z)+f^{3}(z+c)=1$ . Aequat Math, 2017, 91, 129- 136 doi: 10.1007/s00010-016-0443-x
19	Montel P . Leçons Sur les Familles Normales de Fonctions Analytiques et Leurs Applications. Paris: Gauthier-Villars, 1927: 135- 136
20	Steinmetz N . Zur Wertverteilung von exponentialpolynomen. Manuscripta Math, 1978, 26, 155- 167 doi: 10.1007/BF01167971
21	Yang C C . A generalization of theorem of P. Montel on entire functions. Proc Amer Math Soc, 1970, 26, 332- 334 doi: 10.1090/S0002-9939-1970-0264080-X
22	Yang C C , Yi H X . Uniqueness Theory of Meromorphic Functions. Beijing: Science Press, 1995

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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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