| 单位圆上解析系数的高阶复微分方程 |
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| 引用本文： | 曾三桂,龙见仁.单位圆上解析系数的高阶复微分方程[J].数学研究及应用,2020,40(4):387-396. |
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| 作者姓名： | 曾三桂 龙见仁 |
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| 作者单位： | 贵州师范大学数学科学学院, 贵州 贵阳 550025 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11861023; 11501142), 贵州省科技计划项目(Grant No.黔科合平台人才[2018]5769-05), 2016贵州师范大学博士启动基金, 2016贵州省''千''层次创新型人才计划项目,贵州省科学技术基金项目(Grant No.[2015]2112). |
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| 摘 要： | The growth of solutions of the following differential equation ■ is studied, where A_j(z) is analytic in the unit disc D = {z : |z| 1} for j = 0, 1,..., k-1. Some precise estimates of p, q]-order of solutions of the equation are obtained by using a notion of newp, q]-type on coefficients.
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| 关 键 词： | 复微分方程 $[p q]$级 $[p q]$型 解析函数 |
| 收稿时间： | 2019/3/8 0:00:00 |
| 修稿时间： | 2019/5/26 0:00:00 |
Higher Order Complex Differential Equations with Analytic Coefficients in the Unit Disc |
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| Sangui ZENG,Jianren LONG.Higher Order Complex Differential Equations with Analytic Coefficients in the Unit Disc[J].Journal of Mathematical Research with Applications,2020,40(4):387-396. |
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| Authors: | Sangui ZENG Jianren LONG |
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| Institution: | School of Mathematical Science, Guizhou Normal University, Guizhou 550025, P. R. China |
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| Abstract: | The growth of solutions of the following differential equation $$f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f''+A_{0}(z)f=0$$ is studied, where $A_{j}(z)$ is analytic in the unit disc $\mathbb{D}=\{z:|z|<1\}$ for $j=0,1,\ldots,k-1$. Some precise estimates of $p, q]$-order of solutions of the equation are obtained by using a notion of new $p, q]$-type on coefficients. |
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| Keywords: | complex differential equation $[p q]$-order of growth $[p q]$-type analytic function unit disc |
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