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

被引：1

作者：

Chen, Minfeng ^{[1
,2
,3
]}

Gao, Zongsheng ^{[2
,3
]}

Zhang, Jilong ^{[2
,3
]}

机构：

[1] Guangdong Univ Foreign Studies, Sch Math & Stat, Guangzhou 510006, Guangdong, Peoples R China

[2] Beihang Univ, LMIB, Beijing 100191, Peoples R China

[3] Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2019年 / 39卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Non-linear difference equation; meromorphic solution; rational solution; value distribution; GROWTH; ZEROS;

D O I：

10.1007/s10473-019-0419-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 Delta f(z) and divided difference Delta f(z)/f(z) are estimated. Furthermore, we f(z) study the forms of rational solutions of the above equation.

引用

页码：1173 / 1184

页数：12