| 高阶非齐次线性微分方程解的性质 |
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| 引用本文： | 张菡之,陈宗煊.高阶非齐次线性微分方程解的性质[J].华南师范大学学报(自然科学版),2012,44(2):18-0. |
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| 作者姓名： | 张菡之 陈宗煊 |
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| 作者单位： | 1.1.华南师范大学石牌校区数学科学学院 |
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| 摘 要： | 研究了非齐次线性微分方程~$f^{(k)}+A_{k-1}f^{(k-1)}+\cdots+A_df^{(d)}+\cdots+A_0f=F$~的解的增长性及零点,其中~$A_j(j=0,1,\cdots,k-1)$~为有限级整函数, $F$~为无穷级整函数,当存在~$A_d(0 \leq d \leq {k-1})$~满足某些特殊条件时,~得到了上述非齐次线性微分方程解的性质.
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| 关 键 词： | 微分方程 整函数 超级 零点收敛指数 |
| 收稿时间： | 2010-12-24 |
The Properties of Solutions for a Class of Higher Order Nonhomogeneous Linear Differential Equations |
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| ZHANG Hanzhi
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CHEN Zongxuan.The Properties of Solutions for a Class of Higher Order Nonhomogeneous Linear Differential Equations[J].Journal of South China Normal University(Natural Science Edition),2012,44(2):18-0. |
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| Authors: | ZHANG Hanzhi CHEN Zongxuan |
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| Institution: | (School of Mathematics,South China Normal University,Guangzhou 510631,China) |
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| Abstract: | The growth of solutions for the equation f(k)+Ak-1f(k-1)+…+Adf(d)+…+A0f=F is investigated,where Aj(1,2,…,k-1) are entire functions with finite order,F is an entire function with infinite order.If the coefficients Ad(0≤d≤k-1) satisfy certain conditions,the properties of solutions for this equation are obtained. |
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| Keywords: | differential equation entire function hyper-order the exponent of the zero-sequence |
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