Analytic Solutions of an Iterative Functional Differential Equation with State Dependent Delay

被引：0

作者：

Liu, Lingxia ^{[1
]}

机构：

[1] Weifang Univ, Dept Math, Weifang 261061, Shandong, Peoples R China

来源：

SOFTWARE ENGINEERING AND KNOWLEDGE ENGINEERING: THEORY AND PRACTICE, VOL 2 | 2012年 / 115卷

关键词：

Iterative functional equation; analytic solution; state dependent delay; Brjuno condition; resonance;

D O I：

暂无

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

This paper is concerned with a functional differential equation with state dependent delay. By constructing a convergent power series solution of an auxiliary equation, analytic solutions for the original differential equation are obtain. For technical reasons, in previous work the constant alpha given in the Schroder transformation, is required to fulfill that alpha is off the unit circle or lies on the circle with the Diophantine condition. In this paper, we obtain results of analytic solutions in the case of alpha at resonance, i.e., at a root of the unity and the case of alpha near resonance under the Brjuno condition.

引用

页码：9 / 16

页数：8

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