关于方程f''+Af'+Bf=0解的增长性, 其中系数A是一个二阶线性微分方程的解

数学物理学报 ›› 2013, Vol. 33 ›› Issue (1): 46-52.

关于方程f''+Af'+Bf=0解的增长性, 其中系数A是一个二阶线性微分方程的解

吴秀碧¹|伍鹏程²

1.贵州大学贵阳 550025|2.贵州师范大学贵阳 550001

收稿日期:2011-08-25 修回日期:2012-11-23 出版日期:2013-02-25 发布日期:2013-02-25
基金资助:
国家自然科学基金(11171080)和贵州省科学技术基金(黔科合J字LKS[2010]07号)资助

On the Growth of Solutions of f''+Af'+Bf=0, Where A is a Solution of a Second Order Linear Differential Equation

WU Xiu-Bi¹, WU Peng-Cheng²

1.Guizhou University, Guiyang 550025|
2.Guizhou Normal University, Guiyang 550001

Received:2011-08-25 Revised:2012-11-23 Online:2013-02-25 Published:2013-02-25
Supported by:
国家自然科学基金(11171080)和贵州省科学技术基金(黔科合J字LKS[2010]07号)资助

摘要/Abstract

摘要：

设 A(z) 是方程f''+P(z)f=0 的非零解, 其中P(z) 是n 次多项式, B(z) 是一个超越整函数且满足 ρ(B)≤{1/2, 那么方程f''+Af'+Bf=0的每一个非零解都是无穷级. 并且方程 f''+A(z)f=0 两个线性无关解乘积的零点序列收敛指数为无穷.

关键词: 增长级, 线性微分方程, 整函数, 零点收敛指数

Abstract:

Let A(z) be a nontrivial solution of f''+P(z)f=0, where P(z) is a polynomial and let B(z) be a transcendental entire function of order ρ≤1/2. Then every nontrivial solution of f''+A(z)f'+B(z)f=0 is of infinite order. Moreover, the exponent of convergence of zero-sequence of the product of two linearly independent solutions of f''+A(z)f=0 is of infinite.

中图分类号:

34M10

吴秀碧, 伍鹏程. 关于方程f''+Af'+Bf=0解的增长性, 其中系数A是一个二阶线性微分方程的解[J]. 数学物理学报, 2013, 33(1): 46-52.

WU Xiu-Bi, WU Peng-Cheng. On the Growth of Solutions of f''+Af'+Bf=0, Where A is a Solution of a Second Order Linear Differential Equation[J]. Acta mathematica scientia,Series A, 2013, 33(1): 46-52.

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