ON MEROMORPHIC SOLUTIONS OF RICCATI AND LINEAR DIFFERENCE EQUATIONS

doi:10.1016/S0252-9602(13)60077-6

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (5): 1243-1254.doi: 10.1016/S0252-9602(13)60077-6

ON MEROMORPHIC SOLUTIONS OF RICCATI AND LINEAR DIFFERENCE EQUATIONS

张然然^1,2|陈宗煊^2*

1. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China；
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

收稿日期:2012-02-23 修回日期:2012-04-28 出版日期:2013-09-20 发布日期:2013-09-20
通讯作者: 陈宗煊,chzx@vip.sina.com E-mail:zhrr19820315@163.com; chzx@vip.sina.com
基金资助:
This work was supported by National Natural Science Foundation of China (11226090, 11171119) and Guangdong Natural Science Foundation (S2012040006865).

ON MEROMORPHIC SOLUTIONS OF RICCATI AND LINEAR DIFFERENCE EQUATIONS

ZHANG Ran-Ran^1,2, CHEN Zong-Xuan^2*

1. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China；
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received:2012-02-23 Revised:2012-04-28 Online:2013-09-20 Published:2013-09-20
Contact: CHEN Zong-Xuan,chzx@vip.sina.com E-mail:zhrr19820315@163.com; chzx@vip.sina.com
Supported by:
This work was supported by National Natural Science Foundation of China (11226090, 11171119) and Guangdong Natural Science Foundation (S2012040006865).

摘要/Abstract

摘要：

In this paper, meromorphic solutions of Riccati and linear difference equations are investigated. The growth and Borel exceptional values of these solutions are discussed, and the growth, zeros and poles of differences of these solutions are also investigated. Furthermore, several examples are given showing that our results are best possible in certain senses.

关键词: complex difference equation, growth order, Borel exceptional value

Abstract:

Key words: complex difference equation, growth order, Borel exceptional value

中图分类号:

30D35

张然然, 陈宗煊. ON MEROMORPHIC SOLUTIONS OF RICCATI AND LINEAR DIFFERENCE EQUATIONS[J]. 数学物理学报(英文版), 2013, 33(5): 1243-1254.

ZHANG Ran-Ran, CHEN Zong-Xuan. ON MEROMORPHIC SOLUTIONS OF RICCATI AND LINEAR DIFFERENCE EQUATIONS[J]. Acta mathematica scientia,Series B, 2013, 33(5): 1243-1254.

参考文献

[1] Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964

[2] Laine I. Nevanlinna Theory and Complex Differential Equations. Berlin: W de Gruyter, 1993

[3] Ablowitz M, Halburd R G, Herbst B. On the extension of Painlev´e property to difference equations. Nonlinearity, 2000, 13: 889–905

[4] Bergweiler W, Langley J K. Zeros of differences of meromorphic functions. Math Proc Camb Phil Soc, 2007, 142: 133–147

[5] Chen Z X, Huang Z B, Zhang R R. On difference equations relating to Gamma function. Acta Math Sci, 2011, 31B(4): 1281–1294

[6] Chen Z X, Shon K H. On zeros and fixed points of differences of meromorphic functions. J Math Anal Appl, 2008, 344: 373–383

[7] Chen Z X, Shon K H. Value distribution of meromorphic solutions of certain difference Painlev´e equations. J Math Anal Appl, 2010, 364: 556–566

[8] Chen Z X. On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations. Sci China, Ser A, 2011, 54: 2123–2133

[9] Chiang Y M, Feng S J. On the Nevanlinna characteristic of f(z+) and difference equations in the complex plane. Ramanujan J, 2008, 16: 105–129

[10] Halburd R G, Korhonen R. Difference analogue of the lemma on the logarithmic derivative with applica-tions to difference equations. J Math Anal Appl, 2006, 314: 477–487

[11] Halburd R G, Korhonen R. Finite-order meromorphic solutions and the discrete Painlev´e equations. Proc London Math Soc, 2007, 94: 443–474

[12] Heittokangas J, Korhonen R, Laine I, Rieppo J, Hohge K. Complex difference equations of Malmquist type. Comput Methods Funct Theory, 2001, 1: 27–39

[13] Ishizaki K. On difference Riccati equations and second order linear difference equations. Aequat Math, 2011, 81: 185–198

[14] Korhonen R. A new Clunie type theorem for difference polynomials. J Differ Equ Appl, 2011, 17: 387–400

[15] Korhonen R, Ronkainen O. Order reduction method for linear difference equations. Proc Amer Math Soc, 2011, 139(9): 3219–3229

[16] Gol’dberg A A, Ostrovskii I V. The Distribution of Values of Meromorphic Functions. Moscow: Nauki, 1970

ON MEROMORPHIC SOLUTIONS OF RICCATI AND LINEAR DIFFERENCE EQUATIONS

ON MEROMORPHIC SOLUTIONS OF RICCATI AND LINEAR DIFFERENCE EQUATIONS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 9

Metrics

本文评价

推荐阅读 0

[1]	Zongxuan CHEN, Zhibo HUANG, Jun WANG, Xiumin ZHENG. DETECTING THE SLOWLY GROWING SOLUTIONS OF SECOND ORDER LINEAR DIFFERENCE EQUATIONS[J]. 数学物理学报(英文版), 2025, 45(3): 837-854.
[2]	李海绸\|高凌云. MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS[J]. 数学物理学报(英文版), 2015, 35(1): 195-206.
[3]	陈宗煊. ON THE DIFFERENCE COUNTERPART OF BRÜCK´S CONJECTURE[J]. 数学物理学报(英文版), 2014, 34(3): 653-659.
[4]	黄志波, 陈宗煊, 李倩. ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE[J]. 数学物理学报(英文版), 2013, 33(4): 1141-1152.
[5]	高凌云. THE GROWTH ORDER OF SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS[J]. 数学物理学报(英文版), 2013, 33(3): 814-820.
[6]	彭炎红, 孙道椿. EXAMPLES ON EXCEPTIONAL VALUES OF MEROMORPHIC FUNCTIONS[J]. 数学物理学报(英文版), 2011, 31(4): 1327-1336.
[7]	陈宗煊, 黄志波, 张然然. ON DIFFERENCE EQUATIONS RELATING TO GAMMA FUNCTION[J]. 数学物理学报(英文版), 2011, 31(4): 1281-1294.
[8]	高凌云. THE GROWTH OF SOLUTIONS OF SYSTEMS OF COMPLEX NONLINEAR ALGEBRAIC DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2010, 30(3): 932-938.
[9]	张显文. CHARACTERISTIC CONDITIONS FOR THE COMPLETE INFINITESIMAL GENERATORS OF ANALYTIC SEMIGROUPS OF GROWTH ORDER α[J]. 数学物理学报(英文版), 2000, 20(1): 97-103.