| 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,2013,34(3):291~298 |
| 非齐次线性微分方程解的增长性 |
| Growth of Solutions to Nonhomogeneous LinearDifferential Equations |
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| DOI： |
| 中文关键词: 微分方程, 超级, 二级收敛指数, Fabry缺项级数 |
| 英文关键词:Differential equation, Hyper-order, Hyper exponents of convergence,
Fabry gap series |
| 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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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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