[1]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):171-174.
　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):171-174.
点击复制

关于2阶线性微分方程f″+Af'+Bf=0解的增长性()
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:
2013年02期
页码:
171-174
栏目:
出版日期:
2013-03-01

文章信息/Info

Title:
On the Growth of Solutions of the Second Order Linear Differential Equation f"+Af'+Bf =0
作者:
刘旭强;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):
LIU Xu-qiang；YI Cai-feng
关键词:
微分方程; 亚纯函数; 亏值; 无穷级
Keywords:
differential equations; meromorphic function; deficient value; infinite order
分类号:
O174.52
文献标志码:
A
摘要:
运用Nevanlinna值分布的理论和方法,研究了2阶亚纯系数线性微分方程f"+Af'+Bf=0解的增长性,在假设A或B具有有限或无穷亏值的不同条件下,证明了方程的每一非零解的增长级均为无穷.
Abstract:
By using the fundamental theory and method of value distribution of Nevanlinna,the growth of solutions of the second order linear differential equations f ″+Af '+Bf=0 is considered where A(z) and B(z) are meromorphic function.Assuming A(z) or B(z) have a finite or infinite deficient value,it was proved that every solution f0 of the complex differential equation has infinite order.

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] Hille E.Ordinary differential equations in the complex domain [M].New York:Wiley,1976.
[4] Gundersen G G.Finite order solution of second order linear differential equations [J].Trans Amer Math Soc,1988,305(1):415-429.
[5] Hellenstein S,Miles J,Rossi J.On the growth of solutions of f ″+gf '+hf=0 [J].Trans Amer Math Soc,1991,324(2):693-706.
[6] 毛志强.某类二阶微分方程解的增长级与零点 [J].江西师范大学学报:自然科学版,2001,25(4):334-338.
[7] Wu Pengcheng,Zhu Jun.On the growth of solutions of the complex differential equation f ″+Af '+Bf=0 [J].Science China:Mathematics,2011,54(5):939-947.
[8] 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.
[9] Gundersen G G.Estimates for the logarithmic derivative of a meromorphic function,plus similar estimates [J].J London Math Soc,1988,37(1):88-104.
[10] Wu Pengcheng,Wu Shengjian,Zhu Jun.On the growth of solutions of second order complex differential equation with meromorphic coefficients [J].Jourmal of Inequalities and Applications,2012,117:1-13.
[11] 高仕安,陈宗煊,陈特为.线性微分方程的复振荡理论 [M].武汉:华中理工大学出版社,1998.

相似文献/References:

[1]易才凤,李爱平.一类复合差分函数零点的估计[J].江西师范大学学报(自然科学版),2012,(01):41.
　YI Cai-feng,LI Ai-ping.The Estimate on Zeros of Composition Differences of Meromorphic Functions[J].Journal of Jiangxi Normal University:Natural Science Edition,2012,(02):41.
[2]赵小珍.亚纯函数及其导数分担小函数集的唯一性[J].江西师范大学学报(自然科学版),2012,(02):141.
　ZHAO Xiao-zhen.The Uniqueness of Meromorphic Functions and Their Derivatives Weighted-Sharing the Sets of Small Functions[J].Journal of Jiangxi Normal University:Natural Science Edition,2012,(02):141.
[3]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.
[4]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.
[5]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.
[6]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.
[7]肖丽鹏,李明星.单位圆内非齐次线性微分方程的振荡解[J].江西师范大学学报(自然科学版),2013,(02):166.
　XIAO Li-peng,LI Ming-xing.Oscillatory Solutions of Nonhomogeneous Linear Differential Equation in the Unit Disc[J].Journal of Jiangxi Normal University:Natural Science Edition,2013,(02):166.
[8]吴佳,吴芬,陈裕先.向量值亚纯函数的亏量[J].江西师范大学学报(自然科学版),2013,(03):229.
　WU Jia,WU fen,CHEN Yu-xian.Deficiency of Vector Valued Meromorphic Function[J].Journal of Jiangxi Normal University:Natural Science Edition,2013,(02):229.
[9]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.
[10]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.
[11]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.
[12]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.
[13]杨碧珑,易才凤.一类高阶线性微分方程解在角域上的增长性[J].江西师范大学学报(自然科学版),2014,(04):390.
　YANG Bi-long,YI Cai-feng.The Growth of Solutions of a Class Higher Order Linear Differential Equations in Angular Donains[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(02):390.

备注/Memo

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