[1]张建军,李 晶.关于复差分方程和q-差分方程的一些结果[J].南京师范大学学报(自然科学版),2013,36(04):30.
 Zhang Jianjun,Li Jing.Some Results on Complex Difference and q-Difference Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(04):30.
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关于复差分方程和q-差分方程的一些结果
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第36卷
期数:
2013年04期
页码:
30
栏目:
数学
出版日期:
2013-12-31

文章信息/Info

Title:
Some Results on Complex Difference and q-Difference Equations
作者:
张建军1李 晶2
(1.江苏第二师范学院数学与信息技术学院,江苏 南京 210013) (2.南京大学数学系,江苏 南京 210093)
Author(s):
Zhang Jianjun1Li Jing2
(1.School of Mathematics and Information Technology,Jiangsu Second Normal University,Nanjing 210013,China) (2.Department of Mathematics,Nanjing University,Nanjing 210093,China)
关键词:
Wittich定理差分方程增长级亚纯函数
Keywords:
Wittich theoremdifference equationsgrowth ordermeromorphic functions
分类号:
O174.5
文献标志码:
A
摘要:
本文主要证明了复差分方程和q-差分方程的Wittich定理,类似的结果首先出现在复微分方程中.同时本文还给出了q-差分方程的Malmquist型定理.
Abstract:
The main purpose of this paper is to prove difference and q-difference counterparts of the Wittich theorem from complex differential equations.We also give the q-difference analogue of Malmquist type theorem.

参考文献/References:

[1] Barnett D C,Halburd R G,Korhonen R J,et al.Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations[J].Proc Roy Soc Edinburgh Sect A,2007,137:457-474.
[2]Chiang Y M,Feng S J.On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane[J].Ramanujan Journal,2008,16:105-129.
[3]Halburd R G,Korhonen R J.Difference analogue of the lemma on the logarithmic derivative with applications to difference equations[J].J Math Anal Appl,2006,314:477-487.
[4]Laine I,Yang C C.Clunie theorems for difference and q-difference polynomials[J].J London Math Soc,2007,76:556-566.
[5]Cherry W,Ye Z.Nevanlinna’s Theory of Value Distribution[M].Berlin:Springer-Verlag,2001.
[6]Hayman W K.Meromorphic Functions[M].Oxford:Clarendon Press,1964.
[7]Laine I.Nevanlinna Theory and Complex Differential Equations[M].Berlin-New York:Walter de Gruyter,1993.
[8]Wittich H.Neuere untersuchungen(¨overu)ber eindeutige analytische funktionen[M].Berlin-Gottingen-Heidelberg:Springer-Verlag,1955.
[9]Zhang J J,Liao L W.Admissible meromorphic solutions of algebraic differential equations[J].J Math Anal Appl,2013,397:225-232.
[10]Elaydi S.An Introduction to Difference Equtions[M].3rd ed.New York:Springer-Verlag,2005.
[11]Zhang J J,Liao L W.Further extending results of some classes of complex difference and functional equations[J].Advances in Difference Equations,2010,ID404582:1-15.
[12]Mohon’ko A Z.The Nevanlinna characteristics of certain meromorphic functions[J].Teor Funktsiǐ Funktsional Anal i Prilozhen,1971,14:83-87(in Russian).
[13]Mokhon’ko A Z,Mokhon’ko V D.Estimates for the Nevanlinna characteristics of some classes of meromorphic functions and their applications to differential equations[J].Sibirskii Matematicheskii Zhurnal,1974,15:1 305-1 322(in Russian).
[14]Zhang J L,Korhonen R.On the Nevanlinna characteristic of f(qz) and its applications[J].J Math Anal Appl,2010,369:537-544.

相似文献/References:

[1]徐新萍,张建军.关于复差分方程Wittich定理的一个新证明(英文)[J].南京师范大学学报(自然科学版),2015,38(04):22.
 Xu Xinping,Zhang Jianjun.On a New Proof of Wittich Theorem ofComplex Difference Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2015,38(04):22.

备注/Memo

备注/Memo:
Received data:2013-02-16. Foundation item:Supported by the National Natural Science Foundation of China(11271179),the Colonel-Level Topics of Jiangsu Second Normal University(Jsie2012zd01). Corresponding author:Zhang Jianjun,Ph.D,lecturer,majored in complex analysis.E-mail:zhangjianjun1982@163.com
更新日期/Last Update: 2013-12-30