[1]高凌云,刘曼莉.复合函数方程的超越亚纯解[J].江西师范大学学报(自然科学版),2016,40(06):587-590.
 GAO Lingyun,LIU Manli.The Transcendental Meromorphic Solutions of Composite Functional Equations[J].,2016,40(06):587-590.
点击复制

复合函数方程的超越亚纯解()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
40
期数:
2016年06期
页码:
587-590
栏目:
出版日期:
2016-12-01

文章信息/Info

Title:
The Transcendental Meromorphic Solutions of Composite Functional Equations
作者:
高凌云刘曼莉
暨南大学数学系,广东 广州 510632
Author(s):
GAO LingyunLIU Manli
Department of Mathematics,Jinan University,Guangzhou Guangdong 510632,China
关键词:
复合函数方程 超越亚纯解 值分布理论
Keywords:
composite functional equations transcendental meromorphic solutions distribution theory
分类号:
O 174.52
摘要:
利用亚纯函数Nevanlinna值分布理论,研究了一类复合函数方程和一类复合函数方程组的超越亚纯解的性质问题,得到了2个有关复合函数方程和复合函数方程组当给予其系数的极点控制时,其解的特征估计和计数估计,将Silvennoinen的某些结果推广至更为复杂的复合函数方程和复合函数方程组中.举例表明定理中的条件是精确的.
Abstract:
Using the Nevanlinna theory of the value distribution of meromorphic functions,the problem of properties of transcendental solutions of(systems of )composite functional equations are investigated,and characteristic estimate and non-integrated counting estimate of solutions are obtained while restricting the number of the poles of the coefficients,a certain result of Silvennoinen concerning composite functional equations is extened to systems of composite functional equations.Examples show that our condition in Theorems are precise.

参考文献/References:

[1] 仪洪勋.亚纯函数唯一性理论 [M].北京:科学出版社,1995.
[2] 何育赞,肖修治.代数体函数与常微分方程 [M].北京:科学出版社,1988.
[3] Goldstein R.On certain compositions of functions of a complex variable [J].Aequations Math,1970,4(1/2):103-126.
[4] Goldstein R.On meromorphic solutions of a functional equations [J].Aequations Math,1972,8(1):82-94.
[5] Goldstein R.On meromorphic solutions of certain functional equations [J].Aequations Math,1978,18(1/2):112-157.
[6] Goldstein R.Some results on factorisation of meromorphic functions [J].J London Math Soc,1971,4(2):357-364.
[7] Bergweiler W,Ishizaki K,Yanagihara N.Growth of meromorphic solutions of some functional equations I [J].Aequations Math,2002,63(1/2):140-151.
[8] Bergweiler W,Ishizaki K,Yanagihara N.Meromorphic solutions of some functional equations [J].Methods Appl Anal,1998,5(3):248-258.
[9] Heittokangas J,Laine I,Rieppo J,et al.Meromorphic solutions of some linear functional equations [J].Aequations Math,2000,60(1):148-166.
[10] Chen Zongxuan,Shon K H.On zeros and fixed points of differences of meromorphic functions [J].J Math Anal Appl,2008,344(1):373-383
[11] 甘会林.整函数差分的零点和不动点 [J].江西师范大学学报:自然科学版,2015,39(5):519-521.
[12] Silvennoinen H.Meromorphic solutions of some composite functional equations [J].Helsinki,Ann Acad Sci Fenn,Mathematica Dissertations,2003(133):39.
[13] Gao Lingyun.On meromorphic solutions of a type of system of composite functional equations [J].Acta Mathematica Scientia,2012,32B(2):800-806.
[14] Li Haichou,Gao Lingyun.Meromorphic solutions of system of functional equations [J].J of Math,2012,32(4):593-597.
[15] 高凌云.关于一类差分方程的亚纯解 [J].数学年刊,2014,35A(2):193-202.
[16] 高凌云.一类复差分方程组的亚纯解 [J].数学学报,2016,59(3):363-368.
[17] 刘曼莉,高凌云.一类复差分方程组的亚纯解 [J].山东大学学报:理学版,2016,51(10):34-40.

备注/Memo

备注/Memo:
收稿日期:2016-09-06基金项目:国家自然科学基金(11271161)资助项目.作者简介:高凌云(1963-),男,湖北蕲春人,教授,博士,主要从事复分析与复微分方程的研究.
更新日期/Last Update: 1900-01-01