单位圆内高阶非齐次微分方程复振荡与解及其任意阶导数的不动点  

Oscillation and Fixed Points of Solutions and Their Arbitrary-order Derivatives of Higher-order Nonhomogeneous Differential Equations in the Unit Disc

作　　者：陈玉[1] 邓冠铁[2] CHEN Yu;DENG Guantie(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,China;School of Mathematical Sciences,Key Laboratory of Mathematics and Complex Systems of Ministry of Education,Beijing Normal University,Beijing 100875,China)

机构地区：[1]江西师范大学数学与统计学院,江西南昌330022 [2]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

出　　处：《应用数学》2024年第4期1154-1162,共9页Mathematica Applicata

基　　金：国家自然科学基金(11971042,12071035);江西省教育厅科学技术研究项目(GJJ210314);江西师范大学博士科研基金(12021323)。

摘　　要：本文研究一类单位圆内有穷迭代级解析系数的高阶非齐次线性微分方程的复振荡与解及其任意阶导数的不动点问题,得到解的迭代增长级,迭代级零点收敛指数的更精细的估计,并得到解的不动点与解的任意阶导数的不动点分布的精确估计.所得结果是已有相关结果的推广.In this paper,we investigate the oscillation and fixed points of solutions and their arbitrary-order derivatives of higher-order nonhomogeneous linear differential equations with analytic coefficients of finite iterated order in the unit disc.We obtain more precise estimation on the iterated order and iterated convergence exponent for the sequences of zeros of solutions,especially on the distributions of the fixed points of the solutions and their arbitrary-order derivatives.The obtained results are some extension of the previous relevant results.

关 键 词：微分方程 解析函数 单位圆 零点收敛指数 不动点 

分 类 号：O174.5[理学—数学]