[1]钟文波,易才凤.一类高阶线性微分方程解的增长级[J].江西师范大学学报(自然科学版),2014,(04):399-402.
 ZHONG Wen-bo,YI Cai-feng.On the Growth of Solutions of a Class of Higher Order Linear Differential Equations[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(04):399-402.
点击复制

一类高阶线性微分方程解的增长级()
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:
2014年04期
页码:
399-402
栏目:
出版日期:
2014-08-31

文章信息/Info

Title:
On the Growth of Solutions of a Class of Higher Order Linear Differential Equations
作者:
钟文波;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):
ZHONG Wen-bo;YI Cai-feng
关键词:
整函数杨-张不等式微分方程无穷级
Keywords:
entire functionYang-Zhang inequalitydifferential equationsinfinite order
分类号:
O174.52
文献标志码:
A
摘要:
运用 Nevanlinna 值分布的基本理论和整函数的相关性质,研究了一类高阶齐次线性微分方程解的增长性,在假设其系数均为整函数,且有1个满足杨-张不等式的极端情况的条件下,证明了方程的每1个非零解均具有无穷级。
Abstract:
By using the fundamental theory of value distribution of Nevanlinna and the property of entire function, the growth of solutions of the higher order linear differential equations is considered where coefficients are entire function. Assume that one of coefficients is extremal for Yang-Zhang inequality,it was proved that every nontrivial solution 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] 张广厚.整函数和亚纯函数理论 [M].北京:科学出版社,1986.
[4] Yang Le.Deficient values and angular distribution of entire functions [J].Trans Amer Math Soc,1988,308(2):583-601.
[5] Gundersen G G.Finite order solution of second order linear differential equations [J].Trans Amer Math Soc,1988,305(1):415-429.
[6] Hellerstein S,Miles J,Rossi J.On the growth of solutions of f ″+gf '+hf=0 [J].Trans Amer Math Soc,1991,324(2):693-705.
[7] Chen Zongxuan.The growth of solutions of f ″+ef '+Q(z)f=0 where the order(Q)=1 [J].Science in China:A,2002,45(3):290-300.
[8] 刘旭强,易才风.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.
[9] 石磊,易才风.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] Wu Pengcheng,Zhu Jun.On the growth of solutions to the complex differential equation f ″+Af '+Bf=0 [J].Science China:Mathematics,2011,54(5):939-947.
[11] Long Jianren,Wu Pengcheng,Zhang Zheng.On the growth of solutions of second order linear differential equations with extremal coefficients [J].Acta Mathematica Sinica,English Serier,2013,29(2):365-372.
[12] Chen Zongxuan,Gao Shian.The complex oscillation theory of certain non-homogemeous linear differential equations with transcendental entire coefficients [J].Journal of Mathematical Analysis and Applications,1993,179(2):403-416.
[13] Wu Shengjian.Some results on entire functions of finite lower order [J].Acta Math Ematica Sinica,English Series,1994,10(2):168-178.
[14] Gundersen G G.Estimate for the logarithmic derivative of a meromorphic function [J].J London Math Soc,1988,37(1):88-104.
[15] Chen Zongxuan,Yang Chongjun.Quantitative estimates on the zeros and growth of entire solutions of linear differential equations [J].Complex Variables,2000,42(1):119-133.
[16] Barry P D.On a theorem of besicovitch [J].Quant J Math Oxford Ser,1963,14(2):293-302.
[17] Chen Zongxuan,Yang Chongjun.Some further results on the zeros and growths of entire solutions of second order linear differential equations [J].Kodai Math J,1999,22(2):273-285.

相似文献/References:

[1]涂金,刘翠云,徐洪焱.亚纯函数相对于(r)的[p,q]增长级[J].江西师范大学学报(自然科学版),2012,(01):47.
 TU Jin,LIU Cui-yun,XU Hong-yan.Meromorphic Functions of Relative [p,q] Order to (r)[J].Journal of Jiangxi Normal University:Natural Science Edition,2012,(04):47.
[2]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,(04):230.
[3]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,(04):579.
[4]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,(04):233.
[5]闵小花,张红霞,易才凤.2阶微分方程的解与小函数的关系[J].江西师范大学学报(自然科学版),2014,(06):551.
 MIN Xiao-hua,ZHANG Hong-xia,YI Cai-feng.The Relations between Solutions of Second Order Linear Differential Equations with Functions of Small Growth[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(04):551.
[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].Journal of Jiangxi Normal University:Natural Science Edition,2015,(04):340.
[7]涂 金,彭淑凤,饶冬飞.有限对数级亚纯函数与整函数的复合[J].江西师范大学学报(自然科学版),2018,(06):587.[doi:10.16357/j.cnki.issn1000-5862.2018.06.06]
 TU Jin,PENG Shufeng,RAO Dongfei.The Composition of Meromorphic Function and Entire Function of Finite Logarithmic Order[J].Journal of Jiangxi Normal University:Natural Science Edition,2018,(04):587.[doi:10.16357/j.cnki.issn1000-5862.2018.06.06]
[8]涂 金,吕凤恒,江 杰.整函数与解析函数的最大模M(r,f)及其导函数M'(r,f)增长性比较[J].江西师范大学学报(自然科学版),2019,(04):331.[doi:10.16357/j.cnki.issn1000-5862.2019.04.01]
 TU Jin,LYU Fengheng,JIANG Jie.The Comparison on the Growth of the Maximum Moduli M(r,f)and Its Derivative Function M'(r,f)of Entire Function and Analytic Function[J].Journal of Jiangxi Normal University:Natural Science Edition,2019,(04):331.[doi:10.16357/j.cnki.issn1000-5862.2019.04.01]
[9]涂 金,孙合庆,刘 杰.整函数及复合整函数的相对[p,q]级与相对[p,q]型[J].江西师范大学学报(自然科学版),2020,(01):1.[doi:10.16357/j.cnki.issn1000-5862.2020.01.01]
 TU Jin,SUN Heqing,LIU Jie.The Relative[p,q] Order and Relative[p,q] Type of Entire Functions and Composite Entire Functions[J].Journal of Jiangxi Normal University:Natural Science Edition,2020,(04):1.[doi:10.16357/j.cnki.issn1000-5862.2020.01.01]
[10]宁菊红,宋文佩,黄文平.广义Laplace-Stieltjes变换所表示整函数的β级和广义型[J].江西师范大学学报(自然科学版),2020,(06):590.[doi:10.16357/j.cnki.issn1000-5862.2020.06.07]
 NING Juhong,SONG Wenpei,HUANG Wenping.The β Order and Generalized Type of Entire Functions Represented by Generalized Laplace-Stieltjes Transforms[J].Journal of Jiangxi Normal University:Natural Science Edition,2020,(04):590.[doi:10.16357/j.cnki.issn1000-5862.2020.06.07]

备注/Memo

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