Exact and explicit analytic solutions of an extended Jabotinsky functional differential equation

被引：0
|
作者：
Jibin Li
Hanze Liu
Fang Qiu
机构：
[1] Kunming University of Science and Technology,Center for Nonlinear Science Studies, School of Science
[2] Zhejiang Normal University,Department of Mathematics
[3] Binzhou University,Department of Mathematics
[4] Kunming University of Science and Technology,Center for Nonlinear Science Studies, School of Science
来源：
Israel Journal of Mathematics | 2009年 / 174卷
关键词：
Unit Root; Auxiliary Equation; Iteration Theory; Power Series Solution; Diophantine Condition;
D O I：
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学科分类号：
摘要：
In this paper, an extended Jabotinsky-type functional iterative differential equation is investigated in the complex field C for the existence of local analytic solutions. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained. Furthermore, the exact and explicit analytic solution of the original equation is investigated for the first time. We discuss not only the general case, but also critical cases as well, especially for α a unit root, and in case (H4) we deal with the equation under the Brjuno condition, which is weaker than the Diophantine condition. Such equations are important in both applications and the theory of iteration.
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页码：29 / 45
页数：16
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