VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

doi:10.1007/s10473-019-0419-8

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (4): 1173-1184.doi: 10.1007/s10473-019-0419-8

VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

陈敏风^1,2, 高宗升², 张继龙²

1. School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China;
2. LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

收稿日期:2018-06-04 出版日期:2019-08-25 发布日期:2019-09-12
通讯作者: Minfeng CHEN E-mail:chenminfeng198710@126.com
作者简介:Zongsheng GAO,E-mail:zshgao@buaa.edu.cn;Jilong ZHANG,E-mail:jilongzhang2007@gmail.com
基金资助:
This research was supported by the National Natural Science Foundation of China (11371225) and National Natural Science Foundation of Guangdong Province (2016A030313686).

VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

Minfeng CHEN^1,2, Zongsheng GAO², Jilong ZHANG²

1. School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China;
2. LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

Received:2018-06-04 Online:2019-08-25 Published:2019-09-12
Supported by:
This research was supported by the National Natural Science Foundation of China (11371225) and National Natural Science Foundation of Guangdong Province (2016A030313686).

摘要/Abstract

摘要： In this article, we consider the non-linear difference equation
(f(z + 1)f(z)-1)(f(z)f(z-1)-1)=P(z, f(z))/Q(z, f(z)),
where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z) are estimated. Furthermore, we study the forms of rational solutions of the above equation.

关键词: Non-linear difference equation, meromorphic solution, rational solution, value distribution

Abstract: In this article, we consider the non-linear difference equation
(f(z + 1)f(z)-1)(f(z)f(z-1)-1)=P(z, f(z))/Q(z, f(z)),
where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z) are estimated. Furthermore, we study the forms of rational solutions of the above equation.

Key words: Non-linear difference equation, meromorphic solution, rational solution, value distribution

中图分类号:

30D35

陈敏风, 高宗升, 张继龙. VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS[J]. 数学物理学报(英文版), 2019, 39(4): 1173-1184.

Minfeng CHEN, Zongsheng GAO, Jilong ZHANG. VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS[J]. Acta mathematica scientia,Series B, 2019, 39(4): 1173-1184.

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VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

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