| 非齐次线性微分方程解的增长性 |
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| 引用本文： | 蒋业阳,陈宗煊.非齐次线性微分方程解的增长性[J].数学年刊A辑(中文版),2013,34(3):291-298. |
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| 作者姓名： | 蒋业阳 陈宗煊 |
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| 作者单位： | 华南师范大学数学系, 广州 510631;华南师范大学数学系, 广州 510631. |
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| 基金项目： | 国家自然科学基金 (No.11171119)和广东省自然科学基金博士启动基金(No.S2012040006865) |
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| 摘 要： | 研究了非齐次线性微分方程f^{(k)}+A_{k-1}(z)f^{(k-1)}+...+A_{s}(z)f^{(s)}+...+A_{0}(z)f=F(z)
解的增长性,其中A_{j}(j=0,1,\cdots,k-1)及F是整函数. 在A_{s}比其他系数有较快增
长的情况下,得到了上述非齐次微分方程在一定条件下的超越整函数解的超级的精确估计.
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| 关 键 词： | 微分方程 超级 二级收敛指数 Fabry缺项级数 |
Growth of Solutions to Nonhomogeneous Linear
Differential Equations |
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| JIANG Yeyang and CHEN Zongxuan.Growth of Solutions to Nonhomogeneous Linear
Differential Equations[J].Chinese Annals of Mathematics,2013,34(3):291-298. |
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| Authors: | JIANG Yeyang and CHEN Zongxuan |
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| Affiliation: | Department of Mathematics, South China Normal University,
Guangzhou 510631, China.;Department of Mathematics, South China Normal University,
Guangzhou 510631, China. |
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| Abstract: | The authors investigate the growth of solutions to the nonhomogeneous linear differential equation
$f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{s}(z)f^{(s)}+\cdots+A_{0}(z)f=F(z)$, where $A_{j} \ (j=0,1,\cdots,k-1)$ and $F$
are entire functions. When the domain coefficient $A_{s}$ grows faster than other coefficients, the precise estimates
of the hyper-order of transcendental entire solutions to the previous higher order linear differential equation are obtained. |
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| Keywords: | Differential equation Hyper-order Hyper exponents of convergence Fabry gap series |
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