| 一类二阶迭代泛函微分方程解析解的存在性 |
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| 引用本文： | 刘凌霞.一类二阶迭代泛函微分方程解析解的存在性[J].山东大学学报(理学版),2008,43(3):64-69. |
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| 作者姓名： | 刘凌霞 |
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| 作者单位： | 潍坊学院数学系,山东,潍坊,261061 |
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| 摘 要： | 在复数域中讨论二阶迭代泛函微分方程
x″(x［r］(z))=c0z+c1x(z)+…+cmx［m］(z), z∈C,
的解析解,其中r,m是非负整数,c0,c1,…,cm是复值常数,并且x［i］表示x的i次迭代。在α(α表示线性化的特征值)是单位根的情形以及α在共振点附近且满足Brjuno条件的情形,给出了解析解的结果。
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| 关 键 词： | 迭代 泛函微分方程 解析解 优级数 |
| 文章编号： | 1671-9352(2008)03-0064-06 |
| 修稿时间： | 2008年1月2日 |
Existence of analytic solutions of a second-iterative functional differential equation |
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| LIU Ling-xia.Existence of analytic solutions of a second-iterative functional differential equation[J].Journal of Shandong University,2008,43(3):64-69. |
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| Authors: | LIU Ling-xia |
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| Institution: | The Mathematics Departments, Weifang University, Weifang 261061, Shandong, China |
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| Abstract: | Analytic solutions of a second order iterative functional differential equation
x″(x［r］(z))=c0z+c1x(z)+…+cmx［m］(z), z∈C,
were discussed in a complex field, where r and m are nonnegative integers, c0,c1,…,cm are complex constants, and x［i］ is the ith iterated function x(z). The analytic solutions are obtained in the case of unit root α， of which that the linearized eigenvalue α is near resonance under the Brjuno condition. |
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| Keywords: | iteration functional differential equation analytic solution majorant series |
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