| 高阶亚纯函数系数微分方程的解及其导数的不动点 |
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| 引用本文： | 周凤麟,徐洪焱.高阶亚纯函数系数微分方程的解及其导数的不动点[J].数学的实践与认识,2012,42(6):199-205. |
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| 作者姓名： | 周凤麟 徐洪焱 |
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| 作者单位： | 景德镇陶瓷学院信息工程学院,江西景德镇,333403 |
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| 基金项目： | 江西省自然科学(青年)基金,江西省教育厅青年科学基金,景德镇陶瓷学院自选课题 |
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| 摘 要： | 研究了高阶线性微分方程f~(k)+A_(k-1)(z)f~(k-1)+…+A_1(z)f′+A_0(z)f=0的非零解f,及其一阶、二阶导数,f~(i)(i=1,2)的不动点性质,这里A_j(z)(j=0,1,…k-1)为亚纯函数,得到了若δ(∞,A_0)>0,且满足max{i(A1),i(A2),…,i(A_(k-1))}
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| 关 键 词： | 亚纯函数 复微分方程 不动点 |
The Fixed-Point of Solution and its Derivative of the Higher Order Linear Differential Equation with Meromorphic Function Coefficients |
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| ZHOU Feng-lin
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XU Hong-yan.The Fixed-Point of Solution and its Derivative of the Higher Order Linear Differential Equation with Meromorphic Function Coefficients[J].Mathematics in Practice and Theory,2012,42(6):199-205. |
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| Authors: | ZHOU Feng-lin XU Hong-yan |
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| Institution: | (Department of Informatics and Engineering,Jingdezhen Ceramic Institute,Jingdezhen 333403,China) |
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| Abstract: | This paper investigates the properties of the fixed-point of solution f(0) andits derivative f~((i))(i=1,2,…) of higher order linear differential equationf~((k))+ A_(k-1)(z)f~((k-1)) +…+ A_1(z)f' + A_0(z)f = 0where A_j(z)(j = 0,1,…,k -1) are meromorphic functions.And we obtain(?)_(p+1)(f-z)=()_(p+1)(f'-z)=()_(p+1)(f"-z)=σ_(p)(f)≥σ_p(A_0)whenδ(∞,B)>0,and max{i(A_1),i(A_2),…,i(A_(k-1))}
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| Keywords: | meromorphic function entire function complex differential equation fixedpoint |
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