[1]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):335-338.
　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,(04):335-338.
点击复制

一类高阶微分方程解的增长性()
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:
2012年04期
页码:
335-338
栏目:
出版日期:
2012-08-01

文章信息/Info

Title:
On the Growth for Solutions of a Certain Higher Order Differential Equation
作者:
冯斌;刘慧芳;李延玲
江西师范大学数学与信息科学学院, 江西 南昌 330022
Author(s):
FENG Bin;  LIU Hui-fang;  LI Yan-ling
关键词:
微分方程; 增长级; 零点收敛指数; 超级
Keywords:
differential equation;  order of growth;  exponent of convergence;  hyper-order
分类号:
O174.52
文献标志码:
A
摘要:
研究了微分方程() k+()11 k?f A f k?+???++e az n n A f A f A f F 2′1′+bz 0 e=解的增长性,其中 ()0A z 、 ()1A z 、F z 是级小于n的整函数, ()jA z ( () 2,3,,1 j=k?是次数不超过m的多项式, a、b为非零复常数.证明了该)方程的所有解 ()f z 满足 () () ()f f fλλσ===∞, () () ()222f f f nλλσ=== , 至多除去2个例外复数b.
Abstract:
The growth for solutions of a differential equation has been investigated, where , and are entire functions with order less than n, are polynomials with degree no more than m, a and b are nonzero complex numbers, then every solution of the above equation satisfies , , except at most two exceptional complex numbers b.

参考文献/References:

[1] 杨乐. 值分布及其新研究 [M]. 北京: 科学出版社, 1982.
[2] 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.
[3] 何育赞, 萧修治. 代数体函数与常微分方程 [M]. 北京: 科学出版社, 1988.
[4] 仪洪勋, 杨重骏. 亚纯函数唯一性理论 [M]. 北京: 科学出版社, 1995.
[5] Ki-Ho Kwon. Nonexistence of finite order solutions of certain second order linear differential equations [J]. Kodai Math J, 1996, 19: 378-387.
[6] 陈宗煊.一类2阶整函数系数微分方程的增长性 [J]. 数学年刊, 1999, 20A(1): 7-14.
[7] 毛志强. 某类2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.
[8] 涂金, 陈宗煊, 曹廷彬, 等. 某类高阶微分方程解的复振荡 [J]. 江西师范大学学报: 自然科学版, 2005, 29(1): 8-11.
[9] 陈宗煊. 关于微分方程 解的增长性 [J]. 中国科学: A辑, 2001, 9: 775-784.
[10] 刘永, 陈宗煊. 一类高阶微分方程的复振荡 [J]. 华南师范大学学报: 自然科学版, 2009, 11(1): 14-19.

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,(04):230.
[2]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,(04):477.
[3]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,(04):1.
[4]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,(04):171.
[5]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.
[6]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,(04):401.
[7]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,(04):162.
[8]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,(04):250.
[9]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,(04):390.
[10]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.
　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.
[11]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.
[12]龚攀,肖丽鹏.某类高阶复微分方程解的增长性[J].江西师范大学学报(自然科学版),2014,(05):512.
　GONG Pan,XIAO Li-peng.The Growth of Solutions of a Class of Higher Order Complex Differential Equations[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(04):512.

更新日期/Last Update: 1900-01-01