| 单位圆内二阶线性微分方程解的增长性与不动点 |
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| 引用本文： | 陈玉,邓冠铁,黄华平. 单位圆内二阶线性微分方程解的增长性与不动点[J]. 北京师范大学学报(自然科学版), 2021, 57(3): 301-305. DOI: 10.12202/j.0476-0301.2020310 |
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| 作者姓名： | 陈玉 邓冠铁 黄华平 |
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| 作者单位： | 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,100875,北京;江西师范大学数学与统计学院,330022,江西南昌;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,100875,北京;重庆三峡学院数学与统计学院,404020,重庆万州 |
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| 基金项目： | 国家自然科学基金资助项目（11271045,11561031） |
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| 摘 要： | 利用系数特征函数比较的极限形式,研究了单位圆内二阶微分方程解的增长性,给出了系数均为可允许的解析函数时方程所有非零解为无穷级的充分条件,并得到了解的不动点估计的一般性结论．所得结果推广了Heittokangas与曹廷彬的结果．
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| 关 键 词： | 线性微分方程 单位圆 可允许的 特征函数 不动点 |
| 收稿时间： | 2020-08-21 |
Growth and fixed points of solutions for second-order linear differential equations in the unit disc |
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| CHEN Yu,DENG Guantie,HUANG Huaping. Growth and fixed points of solutions for second-order linear differential equations in the unit disc[J]. Journal of Beijing Normal University(Natural Science), 2021, 57(3): 301-305. DOI: 10.12202/j.0476-0301.2020310 |
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| Authors: | CHEN Yu DENG Guantie HUANG Huaping |
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| Affiliation: | 1.School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, 100875, Beijing, China2.School of Mathematics and Statistics, Jiangxi Normal University, 330022, Nanchang, Jiangxi, China3.School of Mathematics and Statistics, Chongqing Three Gorges University, 404020, Wanzhou, Chongqing, China |
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| Abstract: | Growth of solutions for second-order differential equations in the unit disc is investigated through some limit form with a comparison of coefficients’ characteristic functions．Some sufficient conditions are given for every non-zero solution to be of infinite order when coefficients of the equations are admissible．Moreover, a general conclusion is drawn on the fixed points in the solutions．The above results extend upon those of Heittokangas and Cao Tingbin． |
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