[1]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):401-405.
 XU Shu-juan,YI Cai-feng.The Growth and Borel Direction of Solutions of Higher Order Linear Differential Equation in Angular Domains[J].,2013,(04):401-405.
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高阶线性微分方程的解在角域内的增长性及Borel方向()
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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:
2013年04期
页码:
401-405
栏目:
出版日期:
2013-09-01

文章信息/Info

Title:
The Growth and Borel Direction of Solutions of Higher Order Linear Differential Equation in Angular Domains
作者:
许淑娟;易才凤
江西师范大学数学与信息科学学院,江西南昌,330022
Author(s):
XU Shu-juan;YI Cai-feng
关键词:
微分方程角域Borel方向无穷级
Keywords:
differential equationssolutionsangular domainBorel directioninfinite order
分类号:
O174.52
文献标志码:
A
摘要:
主要运用角域上的值分布理论和方法,研究了整系数高阶线性微分方程f(n)+An-1f(n-1)+…+A0f=0的解在角域内的增长性和Borel方向.假定Aj(0≤j≤n-1)满足某些条件,证明了方程的非零解在含有Ao的λ(λ>0)级Borel方向的任意角域内的增长级为无穷,且非零解的无穷级Borel方向与Ao的λ级Borel方向一致.
Abstract:
By using the fundamental theory and method of value distribution in angular domain,it is investigated that growth and Borel direction of solutions in angular domains of the higher order linear differential equation f+An-1f+…+A0f=0 where Aj(j=0,…,n-1)are entire functions.Given some conditions for the coefficients Aj(0≤j≤n-1),it is proved that every solution f0 of the equation is of the infinite order in any angular domain which has λ order Borel direction of A0,and the ∞ order Borel direction of the solution is unanimous with the λ order Borel direction of A0.

参考文献/References:

[1] Hayman W K.Meromorphic function [M].Oxford:Clarendon Press,1964.
[2] 杨乐.值分布论及其新研究 [M].北京:科学出版社,1982.
[3] Wu Shengjian.On the growth of solutions of second order linear differential equations in an angle [J].Complex Variable,1994,24(3/4):241-248.
[4] Xu Junfeng,Yi Hongxun.Growth of the solutions of higher order linear differential equations in an angle [J].J Sys Sci & Math Scis,2008,28(6):702-708.
[5] Chen Zongxuan,Gao Shian.The complex oscillation theory of certain non-homogeneous linear differential equations with transcendental entire coefficients [J].1993,179(2):403-416.
[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,2013,37(2):171-174.
[7] Valiron G.Recherches sur le theoreme de M Borel dans la theorie des fonctions meromorphes [J].Aca Math,1929,52(1):67-92.
[8] 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,2013,37(1):1-5.
[9] Goldberg A A,Ostrovskii I V.The distribution of values of meromorphic functions [M].Moscow:Izdat Nauk.1970.
[10] Nevannlinna R.Uber die eigenschaften meromorpher funktionen in einem winkelraum [J].Acta Soc sci Fenn,1925,50(12):1-45.
[11] Tsuji M.Potential theory in modern function theory [M].Tokyo:Maruzen Co Ltd,1959.
[12] Zheng Jianhua.Value distribution of meromorphic functions [M].Berlin:Springer-Verlag,2010.
[13] Wu Shengjian.Estimates for the logarithmic derivative of a meromorphic function in an angle and their application [C].Tian jin:Proceeding of International Conference on Complex Analysis at the Nankai Institute of Mathematics,1992:235-241.
[14] 张广厚.整函数和亚纯函数理论 [M].北京:科学出版社,1986.
[15] Barry P D.Some theorems related to the cosπρ theorem [J].Proc London Math Soc,1970,21(2):334-360.

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备注/Memo

备注/Memo:
国家自然科学基金(11171170)
更新日期/Last Update: 1900-01-01