全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
-  2018 

有穷对数φ级整函数系数线性微分方程解的增长性
On the Growth of Solutions of Linear Differential Equations with Entire Coefficients of Finite Logarithmic φ Order

DOI: 10.13718/j.cnki.xdzk.2018.08.014

Keywords: 线性微分方程, 整函数, 对数φ, Nevanlinna理论, 增长级
linear differential equation
, entire functions, logarithmic φ order, Nevanlinna theory, order of growth

Full-Text   Cite this paper   Add to My Lib

Abstract:

利用亚纯函数的Nevanlinna理论研究了有穷对数φ级整函数系数线性微分方程解的增长性,得到了解的增长级与系数的对数φ级之间的一些关系.
The growth of solutions of linear differential equations with entire coefficients of finite logarithmic φ order is investigated by using Nevanlinna theory of meromorphic functions, and the relationships between the order of growth of solutions of the equations and the logarithmic φ order of coefficients are obtained

References

[1]  HAYMAN W K. Meromorphic Functions[M]. Oxford: Qxford Mathematical Monographs Clarendon Press, 1964.
[2]  周鉴, 杨丛丽. 一类高阶整函数系数微分方程的复振荡[J]. 贵州师范大学学报(自然科学版), 2016, 34(1): 45-47.
[3]  BELAíDI B. Growth of Meromorphic Solutions of Finite Logarithmic Order of Linear Difference Equations[J]. Fasciculi Math, 2015, 54(1): 5-20. DOI:10.1515/fascmath-2015-0001
[4]  LAINE I. Nevanlinna Theory and Complex Differential Equations[M]. Berlin: W. de. Gruyter, 1993.
[5]  FRANK G, HELLERSTEIN S. On the Meromorphic Solutions of Non-Homogeneous Linear Differential Equations with Polynomial Coefficients[J]. Proc London Math Soc, 1986, 53: 407-428.
[6]  CHYZHYKOV I, HEITTOKANGAS J, R?TTY? J. Finiteness of φ-Order of Solutions of Linear Differential Equations in the Unit Disc[J]. J d' Analyse Math, 2009, 109(1): 163-198. DOI:10.1007/s11854-009-0030-3
[7]  龙见仁, 覃智高, 伍廷蜜. 单位圆上解析函数的对数级[J]. 贵州师范大学学报(自然科学版), 2017, 35(6): 77-81.
[8]  CAO T B, LIU K, WANG J. On the Growth of Solutions of Complex Differential Equation with Entire Coefficients of Finite Logarithmic Order[J]. Math Reports, 2013, 15(2): 249-269.
[9]  何育赞, 肖修治. 代数体函数与常微分方程[M]. 北京: 科学出版社, 1988.
[10]  SHEN X, TU J, XU H Y. Complex Oscillation of a Second-Order Linear Differential Equation with Entire Coefficients of[p, q]-φ Order[J]. Adv Difference Equ, 2014, 2014(1): 1-14. DOI:10.1186/1687-1847-2014-1
[11]  吴渊鸿. [p, q]-φ(r)级整函数在复线性微分方程中的应用[D]. 南昌: 江西师范大学, 2014.
[12]  PETERCHERN T Y. On Meromorphic Functions with Finite Logarithmic Order[J]. Tran Amer Math Soc, 2005, 358(2): 473-489.
[13]  GUNDERSEN G. Estimates for the Logarithmic Derivative of a Meromorphic Function, Plus Similar Estimate[J]. J London Math Soc, 1988, 37(2): 88-104.
[14]  YANG L. Value Distribution Theory[M]. Berlin: Springer-Verlag, 1993.
[15]  HEITTOKANGAS J, KORHONEN R, R?TTY? J. Generalized Logarithmic Derivative Estimates of Gol'dberg-Grinshtein Type[J]. Bull London Math Soc, 2004, 36(1): 105-114. DOI:10.1112/S0024609303002649

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133