| 关于一类高阶齐次线性微分方程解的增长性 |
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| 引用本文： | 金瑾.关于一类高阶齐次线性微分方程解的增长性[J].中山大学学报(自然科学版),2013,52(1):51-54. |
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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(2012GZ10526,2010GZ43286);贵州省毕节地区科研基金资助项目([2011]02) |
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| 摘 要： | 研究了高阶线性齐次微分方程
f (k)+Ak－1(z)Pk－1(e z)f ′ +…+A1(z)P1(ez)f ′ +A0(z)P0(ez)f=0
解的增长性，其中Aj(z)≠0(j=0,1,…,k－1)是整函数,Pj(ez)(j=0,1,…,k－1)是ez的非常数多项式，它们的常数项都为零，且次数不相等。证明了该微分方程的每一个非零解有无穷级。
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| 关 键 词： | 线性微分方程 整函数 增长级 |
| 收稿时间： | 2012-09-14; |
On the Growth of Solutions of Higher Order Homogeneous Linear Differential Equations |
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| JIN Jin.On the Growth of Solutions of Higher Order Homogeneous Linear Differential Equations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2013,52(1):51-54. |
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| Authors: | JIN Jin |
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| Institution: | JIN Jin(Mathematics Department,Bijie University,Bijie 551700,China) |
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| Abstract: | The growth of solutions of higher order homogeneous linear differential equation
f (k)+Ak－1(z)Pk－1(e z)f ′ +…+A1(z)P1(ez)f ′ +A0(z)P0(ez)f=0
is investigated, where Aj(z)≠0(j=0,1,…,k－1) are entire functions,Pj(ez)(j=0,1,…,k－1) are nonconstant polynomials of ez without constant term, and deg P(z) is not equal to deg Q(z). It is showed that the order of growth of each nonzero solution of the above equations is infinite. |
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| Keywords: | linear differential equations entire function order of growth |
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