[1]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):166-170.
 XIAO Li-peng,LI Ming-xing.Oscillatory Solutions of Nonhomogeneous Linear Differential Equation in the Unit Disc[J].,2013,(02):166-170.
点击复制

单位圆内非齐次线性微分方程的振荡解()
分享到:

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

卷:
期数:
2013年02期
页码:
166-170
栏目:
出版日期:
2013-03-01

文章信息/Info

Title:
Oscillatory Solutions of Nonhomogeneous Linear Differential Equation in the Unit Disc
作者:
肖丽鹏;李明星
江西师范大学数学与信息科学学院,江西南昌,330022
Author(s):
XIAO Li-peng;LI Ming-xing
关键词:
单位圆线性微分方程亚纯函数零点收敛指数
Keywords:
unit disclinear differential equationsmeromorphic functionexponent of convergence of zero-sequence
分类号:
O174.52
文献标志码:
A
摘要:
研究了单位圆内高阶非齐次线性微分方程的振荡解,得到了方程f(k)+ak-1f(k-1)+…+a0f=F(a0,a1,…,ak-1,和F是单位圆内的亚纯函数)具有1个振荡解空间,其空间中所有解的零点收敛指数为∞,至多除去1个例外值.
Abstract:
The oscillatory solutions of higher-order nonhomogeneous linear differential equation in the unit disc are discussed.Results concerning the equation f+ak-1f+…+a0f=F(where a0,a1,…,ak-1and F are meromorphic functions in the unit disc),and possessing an oscillatory solution subspace in which all solutions(which at most one exception)have infinite exponent of convergence of zeros are obtained.

参考文献/References:

[1] 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.
[2] Pommerenke C.On the mean growth of the solutions of complex linear differential equations in the disk [J].Complex Variables,1982,1(1): 23-38.
[3] 何育赞,肖治经.单位圆内微分方程f '=a0(z)(f-a1(z))f 的解 [J].中国学术期刊文摘:科技快报,1999(5): 164-166.
[4] 陈宗煊.一类单位圆内微分方程解的性质 [J].江西师范大学学报:自然科学版,2002,26(3):189-190.
[5] 王锦熙,易才凤,徐洪焱.关于单位圆内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,2009,33(2): 194-200.
[6] 王丽,陈宗煊.单位圆内高阶微分方程解的一些结果 [J].华南师范大学学报:自然科学版,2007(3): 8-13.
[7] Hayman W.Meromorphic functions [M].Oxford: Claredon Press,1964.
[8] Yang Le.Value distribution theory [M].Berlin: Spring-Verlag,1993.
[9] Heittokangas J.On complex differential equations in the unit disc [J].Ann Acad Sci Fenn Math:Dissertations,2000,122: 1-54.
[10] 郑秀敏,陈宗煊.单位圆内线性齐次微分方程解与系数的关系及应用 [J].华南师范大学学报:自然科学版,2009(2): 12-15.
[11] Wang Yuefei.Oscillatory solutions of nonhomogeneous linear differential equations [J].Arch Math,1997,68(4): 300-310.

相似文献/References:

[1]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,(06):584.
 HE Jing,ZHENG Xiu-min.The Iterated Order of Meromorphic Solutions of Some Classes of Higher Order Linear Differential Equations[J].,2012,(02):584.
[2]金瑾.单位圆内高阶齐次线性微分方程解与不动点的研究[J].江西师范大学学报(自然科学版),2013,(04):406.
 JIN Jin.The Research on Solutions of Higher Order Homogeneous Linear Differential Equations and Fixed Points in the Unit Disc[J].,2013,(02):406.
[3]涂金,黄海霞,徐洪焱,等.单位圆内亚纯函数与解析函数的级与型[J].江西师范大学学报(自然科学版),2013,(05):449.
 TU Jin,HUANG Hai-xia,XU Hong-yan,et al.The Order and Type of Meromorphic Functions and Analytic Functions in the Unit Disc[J].,2013,(02):449.
[4]占燕燕,肖丽鹏.2阶齐次微分方程的次正规解[J].江西师范大学学报(自然科学版),2014,(02):158.
 ZHAN Yan-yan,XIAO Li-peng.The Subnormal Solutions of Second Order Homogeneous Differential Equations[J].,2014,(02):158.
[5]涂金,魏竞斯,徐洪焱.单位圆内[ p,q]-φ(r)级解析函数与亚纯函数的级与型[J].江西师范大学学报(自然科学版),2015,(02):207.
 TU Jin,WEI Jingsi,XU Hongyan.The Order and Type of Meromorphic Functions and Analytic Functions of [p,q]-φ(r)Order in the Unit Disc[J].,2015,(02):207.
[6]易才凤,钟文波.2阶微分方程f "+ Af '+ Bf =0解的增长性[J].江西师范大学学报(自然科学版),2015,(04):340.
 YI Caifeng,ZHONG Wenbo.On the Growth of Solution to the Second Order Differential Equation f " +Af ' +Bf =0[J].,2015,(02):340.
[7]罗丽琴,郑秀敏.具[p,q]-φ级亚纯系数的2阶线性微分方程解的复振荡[J].江西师范大学学报(自然科学版),2016,40(04):331.
 LUO Liqin,ZHENG Xiumin.The Complex Oscillation of a Second Order Linear Differential Equation with Meromorphic Coefficients of [p,q]-φ Order[J].,2016,40(02):331.
[8]龙见仁,伍鹏程.单位圆上高阶线性微分方程解的性质[J].江西师范大学学报(自然科学版),2012,(02):147.
 LONG Jian-ren,WU Peng-cheng.On the Properities of Solutions for Higher Order Linear Differenrial Equations in the Unit Disc[J].,2012,(02):147.
[9]占美龙,郑秀敏.关于单位圆内亚纯系数线性微分方程解的微分多项式的值分布[J].江西师范大学学报(自然科学版),2014,(05):506.
 ZHAN Mei-long,ZHENG Xiu-min.The Value Distribution of Differential Polynomials Generated by Solutions of Linear Differential Equations with Meromorphic Coefficients in the Unit Disc[J].,2014,(02):506.

备注/Memo

备注/Memo:
国家自然科学基金(11126144,11171119);江西省教育厅青年科学基金(GJJ12207)
更新日期/Last Update: 1900-01-01