复微分方程解的增长性及解在若干函数空间的条件

数学物理学报 ›› 2020, Vol. 40 ›› Issue (6): 1481-1491.

复微分方程解的增长性及解在若干函数空间的条件

阳卫锋()

湖南工程学院计算科学与电子学院湖南湘潭 411104

收稿日期:2019-05-24 出版日期:2020-12-26 发布日期:2020-12-29
作者简介:阳卫锋, E-mail: yangweifeng09@163.com
基金资助:
湖南省自然科学基金(2016JJ6029);湖南省教育厅科研基金(16B061)

The Growth and Conditions of Solutions in Some Function Spaces for Complex Linear Differential Equations

Weifeng Yang()

School of Computational Science and Electronics, Hunan Institute of Engineering, Hunan Xiangtan 411104

Received:2019-05-24 Online:2020-12-26 Published:2020-12-29
Supported by:
the Hunan Provincial Natural Science Foundation(2016JJ6029);the Scientific Research Fund of Hunan Provincial Education Department(16B061)

摘要/Abstract

摘要：

讨论了复平面单位圆盘内复线性微分方程 $ f^{(k)}+A_{k-1}(z) f^{(k-1)}+\cdots+A_1(z) f'+A_0(z) f=0, z\in{\mathbb D} $ 解函数与系数函数的关系, 获得了解函数新的增长估计, 以及解函数属于解析函数空间$H_q^{\infty}$, $F (p, q, s)$, ${\cal N}^p_\alpha$的条件.

关键词: 复线性微分方程, 加权Hardy空间, F(p, q, s)空间, 解的增长性

Abstract:

In this paper, the relationship between the solutions and coefficients of the complex linear differential equation (3.13) $f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots +A_1(z)f'+A_0(z)f=0, z\in {\mathbb D}$ is investigated. A new growth estimate of the solutions is provided. Some sufficient conditions on the coefficients are also obtained such that all solutions belong to the $H_q^\infty$ space, the $F(p, q, s)$ space and the ${\cal N}^p_\alpha$ space.

Key words: Complex linear differential equation, Weighted Hardy space, F(p, q, s) space, Growth of solution

中图分类号:

O174.5

阳卫锋. 复微分方程解的增长性及解在若干函数空间的条件[J]. 数学物理学报, 2020, 40(6): 1481-1491.

Weifeng Yang. The Growth and Conditions of Solutions in Some Function Spaces for Complex Linear Differential Equations[J]. Acta mathematica scientia,Series A, 2020, 40(6): 1481-1491.

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