[1]熊辉,刘慧芳.系数为迭代级整函数的高阶线性微分方程的复振荡[J].江西师范大学学报(自然科学版),2015,(02):211-214.
 XIONG Hui,LIU Huifang.The Complex Oscillation of Higher Order Linear Differential Equations with Coefficients of Finite Iterated Order[J].,2015,(02):211-214.
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系数为迭代级整函数的高阶线性微分方程的复振荡()
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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:
2015年02期
页码:
211-214
栏目:
出版日期:
2015-04-10

文章信息/Info

Title:
The Complex Oscillation of Higher Order Linear Differential Equations with Coefficients of Finite Iterated Order
作者:
熊辉;刘慧芳
江西师范大学数学与信息科学学院,江西 南昌 330022
Author(s):
XIONG HuiLIU Huifang
关键词:
微分方程 整函数 迭代级 迭代零点收敛指数
Keywords:
differential equation entire function iterated order iterated convergence exponent of zero sequence
分类号:
O 174.52
文献标志码:
A
摘要:
研究具有迭代级整函数系数的高阶线性微分方程解的增长性和零点问题.当存在某一系数起主导作用时,得到方程解的迭代级和迭代零点收敛指数的估计,推广了已有的结论.
Abstract:
The growth and zeros of solutions of higher order linear differential equations with entire coefficients of finite iterated order are studied.Some estimations on the iterated order and the iterated convergence exponent of zero sequence are obtained,when there exists one dominant coefficients.The obtained results are extensions of some previous results.

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] Laine I.Nevanlinna theory and complex differential equations [M].Berlin:W de Gruyter,1993.
[3] Kinnunen L.Linear differential equations with solutions of finite iterated order [J].Southeast Asian Bull Math,1998,22(4):385-405.
[4] 何静,郑秀敏.几类高阶线性微分方程亚纯解的迭代级 [J].江西师范大学学报:自然科学版,2012,36(6):584-588.
[5] Gundersen G.Finite order solutions of second order linear differential equations [J].Trans Amer Math Soc,1988,305:415-429.
[6] Hellerstein S,Mile J,Rossi J.On the growth of solutions of f ″+gf '+hf=0 [J].Trans Amer Math Soc,1991,324:693-706.
[7] Laine I,Wu Pengcheng.Growth of solutions of second order linear differential equations [J].Proc Amer Math Soc,2000,128:2693-2703.
[8] Kwon K,Kim J.Maximum modulus,characteristic,deficiency and growth of solutions of second order linear differential equations [J].Kodai Math J,2001,24:344-351.
[9] 石磊,易才凤.一类高阶线性微分方程解的增长性 [J].江西师范大学学报:自然科学版,2012,36(3):230-233.
[10] Rong Chang,Cai Huiping,Wang Jun.Growth of nonhomogenous higher order linear differential equations [J].Journal of Fudan University,2011,50(1):47-51.
[11] Hayman W,Rossi J.Characteristic,maximum modulus and value distribution [J].Trans Amer Math Soc,1984,284:651-664.
[12] Murai T.The deficiency of entire functions with Fejér gaps [J].Ann Inst Fourier,1983,33:39-58.
[13] Gundersen G.Estimates for the logarithmic derivative of a meromorphic function,plus similar estimates [J].J London Math Soc,1988,12:88-104.
[14] Tu Jin,Xu Hongyan,Liu Huaming,et al.Complex oscillation of higher-order linear differential equations with coefficients being lacunary series of finite iterated order [J].Abstract and Applied Analysis,2013,2013:1-8.
[15] Cao Tingbin,Xu Junfeng,Chen Zongxuan.On the meromorphic solutions of linear differential equations on the complex plane [J].J Math Anal Appl,2010,364:130-142.

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备注/Memo

备注/Memo:
国家自然科学基金(11201195);江西省自然科学基金(20122BAB201012)
更新日期/Last Update: 1900-01-01