摘要
利用亚纯函数的Nevanlinna的基本理论和方法,研究了系数是单位圆内的高阶齐次和非齐次线性微分方程解的复振荡,讨论了系数是单位圆内的解析函数的高阶齐次和非齐次线性微分方程的解及一次导数和二次导数与其小函数之间的关系,得到了单位圆内高阶齐次和非齐次线性微分方程的解取小函数的精确估计,推广和改进了以前一些文献的结论。
In this paper, we applied the Nevanlinna value distribution theory and methods and investigated the complex oscillation of the higher order： the homogeneous and nonhomogeneous linear differential equations whose coefficients are analytic functions in the unit disc. We also investigate the relation between solutions of the higher order homogeneous and nonhomogeneous linear differential equation with coefficients are analytic functions in the unit disc and their smaller functions, growth. We obtain some precise estima-tions between 1st and 2nd derivatives the solution of the higher orderhomogeneous and nonhomogeneous linear differential equation with coefficients are analytic functions in the unit disc and their smaller functions, which has generalized and improved some known results.
出处
《重庆师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第6期69-76,共8页
Journal of Chongqing Normal University:Natural Science
基金
贵州省科学技术基金(No.2010GZ43286)
贵州省科学技术基金(No.2012GZ10526)
贵州省毕节市科研基金(No.[2011]02)
关键词
单位圆
高阶线性微分方程
小函数
解析函数
超级
收敛指数
unit disc
higher order linear differential equations
small functions
analytic function
hyper order
exponent of conver-gence
