| 一类高阶线性微分方程解的复振荡性质 |
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| 引用本文： | 金瑾.一类高阶线性微分方程解的复振荡性质[J].曲靖师范学院学报,2011,30(3):11-16. |
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| 作者姓名： | 金瑾 |
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| 作者单位： | 毕节学院数学系,贵州毕节,551700 |
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| 基金项目： | 贵州省科学技术基金资助项目(2010GZ43286); 贵州省教育厅科研基金资助项目(2007079) |
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| 摘 要： | 研究了高阶线性微分方程f(k)+Ak-1(z)epk-1(z)f(k-1)+Ak-2(z)epk-2(z)f(k-2)+…+A0(z).ep0(z)f=0和f(k)+Ak-1(z)epk-1(z)f(k-1)+Ak-2(z)epk-2(z)f(k-2)+…+A0(z)ep0(z)f=F(z)解的增长性问题,其中pj(z)=ajzn+bj,1zn-1+…+bj,n,Aj(z)和F(z)是有限级整函数.针对pj(z)中aj(j=0,1,…,k-1)的幅角主值不全相等的情形,得到了方程解的增长级的精确估计.
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| 关 键 词： | 线性微分方程 增长级 整函数 复振荡 |
Properties of Complex Oscilition of the Solutions to Higher Order Linear Differential Equations |
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| Jin Jin.Properties of Complex Oscilition of the Solutions to Higher Order Linear Differential Equations[J].Journal of Qujing Normal College,2011,30(3):11-16. |
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| Authors: | Jin Jin |
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| Institution: | Jin Jin(Department of Mathematics,Bijie University,Bijie Guizhou 551700,P.R.China) |
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| Abstract: | The properties of growth of solutions to Higher Order Linear Differential equations f（k）＋Ak-1（z）epk-1（z）f（k-1）＋…＋A1（z）ep1（z）f′＋A0（z）ep0（z）f=0andf（k）＋Ak-1（z）epk-1（z）f（k-1）＋…＋A1（z）ep1（z）f′＋A0（z）ep0（z）f=F（z）,in the pj（z）=ajzn＋bj,1zn-1＋…＋bj,n are investigated |
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| Keywords: | linear differential equations entire function order of growth complex oscilition |
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