| 范水平,陈宗煊.一类二阶线性微分方程解的增长性[J].数学年刊A辑,2016,37(1):31~40 |
| 一类二阶线性微分方程解的增长性 |
| On the Growth of Solutions to Some Second Order Linear Differential Equations |
| Received:January 10, 2015 Revised:May 08, 2015 |
| DOI： |
| 中文关键词: 微分方程, 整函数, 超级 |
| 英文关键词:Differential equation, Entire function, Hyper order |
| 基金项目:本文受到国家自然科学基金(No.11171119)和广东省自然科学基金项目(No.2014A030313422)的资助 |
|
| Hits: 1750 |
| Download times: 22 |
| 中文摘要: |
| 本文研究一类二阶齐次线性微分方程$$f''+A_{1 (z)\rme^{P(z) f'+A_{0 (z)\rme^{Q(z) f=0$$解的增长性, 其中$P(z)=az^{n $, $Q(z)=bz^{n $,
$ab\neq{0 $, $a=cb~(c>1)$, $A_{j (z)\ (j=0, 1)$是非零多项式,
证明了该方程的每个非零解满足$\sigma(f)=\infty$并且$\sigma_2(f)=n$. |
| 英文摘要: |
| The authors investigate the growth of solutions to some second-order differential equations
\begin{align*}
f''+A_{1}(z)\rme^{P(z)}f'+A_{0}(z)\rme^{Q(z)}f=0,
\end{align*}
where $P(z)=az^{n}$, $Q(z)=bz^{n}$, $ab\neq{0}$,
$a=cb~(c>1)$, and $A_{j}(z)\ (j=0, 1)$ are non-zero polynomials.
It is obtained that every non-zero solution $f$ of the above equation satisfies $\sigma(f)=\infty$ and $\sigma_{2}(f)=n$. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
