周期微分方程的解生成的微分多项式与小函数的关系

数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 562-572.

周期微分方程的解生成的微分多项式与小函数的关系

肖丽鹏

江西师范大学数学与信息科学学院南昌 330022

收稿日期:2012-06-25 修回日期:2013-10-14 出版日期:2014-06-25 发布日期:2014-06-25
基金资助:
国家自然科学基金(11126144, 11171119, 11301232)、江西省自然科学基金(20132BAB211009)和江西省教育厅青年科学基金(GJJ12207) 资助

Relation Between Small Functions with Differential Polynomials Generated by Solution of Periodic Differential Equations

XIAO Li-Peng

Institute of Mathematics and Informations, Jiangxi Normal University, Nanchang |330022

Received:2012-06-25 Revised:2013-10-14 Online:2014-06-25 Published:2014-06-25
Supported by:
国家自然科学基金(11126144, 11171119, 11301232)、江西省自然科学基金(20132BAB211009)和江西省教育厅青年科学基金(GJJ12207) 资助

摘要/Abstract

摘要：

该文研究了某类二阶非齐次周期微分方程的次正规解的存在性, 解的增长性及振荡性.同时也研究了由上述方程的解生成的
微分多项式L(f)=d₂f''+d₁f'+d₀f与小函数的关系, 其中d₀(z), d₁(z), d₂(z)为整函数, 不同时为0.

关键词: 期微分方程, 次正规解, 超级

Abstract:

In this paper, the existence of subnormal solution, the growth and the oscillation of solutions of certain second-order nonhomogeneous periodic differential equation are investigated. Also, the relationship between small functions and differential polynomials L(f)=d₂f''+d₁f'+d₀f generated by solutions of the above equation, where d₀(z), d₁(z), d₂(z) are entire functions that are not all equal to zero, is studied.

Key words: Periodic differential equation, Subnormal solution, Hyper-order

中图分类号:

30D35

肖丽鹏. 周期微分方程的解生成的微分多项式与小函数的关系[J]. 数学物理学报, 2014, 34(3): 562-572.

XIAO Li-Peng. Relation Between Small Functions with Differential Polynomials Generated by Solution of Periodic Differential Equations[J]. Acta mathematica scientia,Series A, 2014, 34(3): 562-572.

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