[1]吴丽镐.一类微差分方程整函数解的性质[J].江西师范大学学报(自然科学版),2018,(06):582-586.[doi:10.16357/j.cnki.issn1000-5862.2018.06.05]
 WU Lihao.The Properties of Entire Solutions of a Certain Type of Differential-Difference Equations[J].,2018,(06):582-586.[doi:10.16357/j.cnki.issn1000-5862.2018.06.05]
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一类微差分方程整函数解的性质()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2018年06期
页码:
582-586
栏目:
复分析研究
出版日期:
2018-12-20

文章信息/Info

Title:
The Properties of Entire Solutions of a Certain Type of Differential-Difference Equations
文章编号:
1000-5862(2018)06-0582-05
作者:
吴丽镐
华南理工大学广州学院计算机工程学院,广东 广州 510800
Author(s):
WU Lihao
School of Computer Engineering,Guangzhou College of South China University of Technology, Guangzhou Guangdong 510800,China
关键词:
微差分方程 整函数 收敛指数
Keywords:
differential-difference equations entire functions exponent of convergence
分类号:
O 174.52
DOI:
10.16357/j.cnki.issn1000-5862.2018.06.05
文献标志码:
A
摘要:
利用值分布理论对一类微差分方程f(z)n+P(f)=β1eα1z2eα2z3eα3z的整函数解的存在性、增长性和零点收敛指数进行了研究,其中αii(i=1,2,3)为复常数,P(f)为f(z)的1阶微差分多项式,并推广了已有的一些结论.
Abstract:
By using the value distribution theory,the existence,growth and exponent of convergence of zeros of entire solutions of a certain type of differential-difference equations of the form f(z)n+P(f)=β1eα1z2eα2z3eα3z are considered,where αii(i=1,2,3) are constants.P(f) denotes an algebraic differential-difference polynomial in f(z) of degree one.And some known results obtained most recently are improved.

参考文献/References:

[1] 杨乐.值分布论及其新研究[M].北京:科学出版社,1982.
[2] Hayman W K.Meromorphic functions[M].Oxford:Clarendon Press,1964.
[3] Chen Zongxuan.Complex differences and difference equations[M].Beijing:Science Press,2014.
[4] 陈宗煊,黄志波.复域差分和差分方程的研究[J].华南师范大学学报:自然科学版,2013,45(6):26-33.
[5] Chen Zongxuan,Yang Chungchun.On entire solutions of certain type of differential-difference equations[J].Taiwanese Journal of Mathematics,2014,18(3):677-685.
[6] Gromak V,Laine I,Shimomura S.Painleve diferential equations in the complex plane[M].Berlin,New York:Waiter de Gruyter,2002.
[7] Laine I.Nevanlinna theory and complex differential equations[M].Berlin:Walter de Gruyter,1993.
[8] 吴丽镐,杨春侠.一类微差分方程亚纯解的性质[J].南昌大学学报:理科版,2017,41(4):316-323.
[9] 张建军,徐新萍,廖良文.非线性复微分方程的亚纯解[J].中国科学:数学,2017,47(8):919-932.
[10] Li Ping,Yang Chungchun.On the nonexistence of entire solutions of a certain type of nonlinear differential equations[J].Journal of Mathematical Analysis and Applications,2006,320(2):827-835.
[11] Zhang Jie,Liao Liangwen.On entire solutions of a certain type of nonlinear differential and difference equations[J].Taiwanese Journal of Mathematics,2011,15(5):2145-2157.
[12] Liao Liangwen,Yang Chungchun,Zhang Jianjun.On meromorphic solutions of certain type of non-linear differential equations[J].Ann Acad Sci Fenn Math,2013,38(2):581-593.
[13] Laine I,Yang Chungchun.Clunnie theorems for difference and q-difference polynomials[J].London Math Soc,2007,76(3):556-566.
[14] Gross F.Factorization of meromorphic functions[M].Washington D C:U S Government Printing Office,1972.
[15] Halburd R,Korhonen R,Toghe K.Holomorphic curves with shift-invariant hyper-plane preimages[J].Transactions of the American Mathematical Society,2014,366(8):4267-4298.
[16] Yang Chungchun,Yi Hongxun.Uniqueness theory of meromorphic functions[M].Dordrecht:Kluwer Academic Publishers Group,2003.
[17] Zhang Ranran,Chen Zongxuan.Fixed points of meromorphic functions and of their differences,divided differences and shifts[J].Acta Mathematica Sinica:English Series,2016,32(10):1189-1202.

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备注/Memo

备注/Memo:
收稿日期:2018-06-15
基金项目:国家自然科学基金(11761035)和广东省普通高校青年创新人才(2015KQNCX230)资助项目.
作者简介:吴丽镐(1982-),男,广东汕头人,副教授,主要从事复分析研究.E-mail:wulh@gcu.edu.cn
更新日期/Last Update: 2018-12-20