单位圆内一类解析系数的二阶线性微分方程解的增长性与不动点  

Growth and fixed points of solutions of a second order linear differential equation with analytic coefficients in the unit disc

作　　者：陈玉 邓冠铁[1] CHEN Yu;DENG Guantie(School of Mathematical Sciences,Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University,100875,Beijing,China;School of Mathematics and Informatics,Jiangxi Normal University,330022,Nanchang,Jiangxi,China)

机构地区：[1]北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,北京100875 [2]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《北京师范大学学报（自然科学版）》2018年第6期687-694,共8页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11271045,11561031).

摘　　要：研究了一类二阶线性微分方程f″+A(z)f′+B(z)f=0的解的性质,式中A(z)和B(z)是单位圆Δ={z:|z|<1}内的解析函数,得到了解的增长级、超级的精确估计,并得到了解及其一阶、二阶导数的不动点的精确估计.The properties of solutions of a second order linear differential equation,f″+A(z)f′+B(z)f=0,where A(z)and B(z)are analytic functions in the unit disc△={z:|z|<1),are investigated.We obtain some precise estimates of growth and hyper order of solutions,fixed points of the solutions and their 1st,2nd derivatives of the equations.

关 键 词：线性微分方程 单位圆 解析函数 不动点 超级 

分 类 号：O174.52[理学—数学]