The properties of the meromorphic solutions of some difference equations

被引：4

作者：

Huang, Zhi-Bo ^{[1
,2
]}

Chen, Zong-Xuan ^{[1
]}

Li, Qian ^{[3
]}

机构：

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] Univ Eastern Finland, Dept Math & Phys, Joensuu 80101, Finland

[3] South China Agr Univ, Dept Appl Math, Guangzhou 510640, Peoples R China

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2013年 / 58卷 / 07期

基金：

中国国家自然科学基金;

关键词：

growth; difference equations; deficiency; fixed points; POLYNOMIALS; ORDER; GROWTH; LEMMA; ZEROS;

D O I：

10.1080/17476933.2011.633302

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we treat complex difference equation of the form A(n)(z)f (z)+n+ center dot center dot center dot +A(1)(z)f (z) A(0)(z)f (z) = A(n+1)(z), where A(j)(z)(j=0,1,...,n,n+1) are meromorphic functions. We give answers to the growth estimates of the meromorphic solutions, and firstly consider the deficiency and fixed points of the meromorphic solutions of these equations. Some examples are listed to show that the result about the properties of fixed points is the best possible in a certain sense.

引用

页码：1023 / 1036

页数：14

共 19 条

[1] On the extension of the Painleve property to difference equations [J].

Ablowitz, MJ ;

Halburd, R ;

Herbst, B .

NONLINEARITY, 2000, 13 (03) :889-905

[2]

[Anonymous], 1964, OXFORD MATH MONOGRAP

[3] Zeros of differences of meromorphic functions [J].

Bergweiler, Walter .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2007, 142 :133-147

[4] On zeros and fixed points of differences of meromorphic functions [J].

Chen, Zong-Xuan ;

Shon, Kwang Ho .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 344 (01) :373-383

[5]

Chen ZX, 2011, ACTA MATH SCI, V31, P627

[6]

[陈宗煊 CHEN Zongxuan], 2006, [数学年刊. A辑, Chinese Annals of Mathematics, Ser. A], V27, P431

[7] On the Hyper-Order of solutions of some second-order linear differential equations [J].

Chen, ZX .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2002, 18 (01) :79-88

[8] On the growth of solutions of a class of higher order differential equations [J].

Chen, ZX ;

Shon, KH .

ACTA MATHEMATICA SCIENTIA, 2004, 24 (01) :52-60

[9] On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane [J].

Chiang, Yik-Man ;

Feng, Shao-Ji .

RAMANUJAN JOURNAL, 2008, 16 (01) :105-129

[10]

Gao S. A., 1998, OSCILLATION THEORY L

← 1 2 →