[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].Journal of Jiangxi Normal University:Natural Science Edition,2015,(02):211-214.
点击复制

系数为迭代级整函数的高阶线性微分方程的复振荡()
分享到：

《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 Hui; LIU 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.

相似文献/References:

[1]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,(03):230.
　SHI Lei,YI Cai-feng.The Growth of Solutions for a Class Higher Order Linear Differential Equations[J].Journal of Jiangxi Normal University:Natural Science Edition,2012,(02):230.
[2]冯斌,刘慧芳,李延玲.一类高阶微分方程解的增长性[J].江西师范大学学报(自然科学版),2012,(04):335.
　FENG Bin,LIU Hui-fang,LI Yan-ling.On the Growth for Solutions of a Certain Higher Order Differential Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2012,(02):335.
[3]杨碧珑,易才凤.一类亚纯系数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,(05):477.
　YANG Bi-long,YI Cai-feng.The Growth for Solutions of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficient[J].Journal of Jiangxi Normal University:Natural Science Edition,2012,(02):477.
[4]李延玲,刘慧芳,冯斌.微分方程f′′+A_1(z)e~(az~n)f′+A_0(z)e~(bz~n)f=F(z)的复振荡[J].江西师范大学学报(自然科学版),2012,(06):579.
　LI Yan-ling,LIU Hui-fang,FENG Bin.On the Complex Oscillation of Differential Equations[J].Journal of Jiangxi Normal University:Natural Science Edition,2012,(02):579.
[5]易才凤,刘旭强.方程f″+Af'+Bf=0的解在角域内的增长性及Borel方向[J].江西师范大学学报(自然科学版),2013,(01):1.
　YI Cai-feng,LIU Xu-qiang.The Growth and Borel Direction of Solutions for Differential Equation f" + Af' + Bf =0 in Angular Domains[J].Journal of Jiangxi Normal University:Natural Science Edition,2013,(02):1.
[6]刘旭强,易才凤.关于2阶线性微分方程f″+Af'+Bf=0解的增长性[J].江西师范大学学报(自然科学版),2013,(02):171.
　LIU Xu-qiang,YI Cai-feng.On the Growth of Solutions of the Second Order Linear Differential Equation f"+Af'+Bf =0[J].Journal of Jiangxi Normal University:Natural Science Edition,2013,(02):171.
[7]安蕾,肖丽鹏.一类2阶微分方程的解和小函数的关系[J].江西师范大学学报(自然科学版),2013,(03):233.
　AN Lei,XIAO Li-peng.The Relation between Solutions of a Class of Second Order Differential Equation with Functions of Small Growth[J].Journal of Jiangxi Normal University:Natural Science Edition,2013,(02):233.
[8]许淑娟,易才凤.高阶线性微分方程的解在角域内的增长性及Borel方向[J].江西师范大学学报(自然科学版),2013,(04):401.
　XU Shu-juan,YI Cai-feng.The Growth and Borel Direction of Solutions of Higher Order Linear Differential Equation in Angular Domains[J].Journal of Jiangxi Normal University:Natural Science Edition,2013,(02):401.
[9]胡军,易才凤.高阶非齐次线性微分方程解沿径向的振荡性质[J].江西师范大学学报(自然科学版),2014,(02):162.
　HU Jun,YI Cai-feng.The Radial Oscillation of Higher Order Non-Homogeneous Linear Differential Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(02):162.
[10]艾丽娟,易才凤.一类亚纯系数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),2014,(03):250.
　AI Li-juan,YI Cai-feng.The Growth for Solutions of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficients[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(02):250.
[11]涂鸿强,刘慧芳.一类2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),2017,(02):184.
　TU Hongqiang,LIU Huifang.On Growth of Solutions of Some Second Order Linear Differential Equations[J].Journal of Jiangxi Normal University:Natural Science Edition,2017,(02):184.

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