一类中立型泛函微分方程周期解的存在性与唯一性

陈志彬;黄立宏

系统科学与数学 ›› 2011, Vol. 31 ›› Issue (4) : 489-500.

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系统科学与数学 ›› 2011, Vol. 31 ›› Issue (4) : 489-500. DOI: 10.12341/jssms10379
论文

一类中立型泛函微分方程周期解的存在性与唯一性

    陈志彬(1)(2), 黄立宏(2)
作者信息 +

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A CLASS OFFUNCTIONAL NEUTRAL DIFFERENTIAL EQUATIONS

    CHEN Zhibin(1)(2), HUANG Lihong(2)
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摘要

利用Schauder不动点理论, 引入线性变换, 用逆变换的思想, 定性与定量地研究一类中立型泛函微分方程周期解的问题, 获得了这一类泛函微分方程周期解存在性与唯一性的充分条件. 我们的研究方法异于相关文献中常用的方法.

Abstract

This paper is concerned with the existence and the uniqueness of periodic solutions for a class of neutral differential functional equations as follows ddt(x(t)−∑i=1ncix(t−τi))=−a(t)x(t)+b(t)f(x(t))+∑i=1nbi(t)f(x(t−σi(t)))+p(t).
By analyzing some properties of operator A:XT(M)→XT(M), (Ax)(t)=x(t)−∑i=1ncix(t−τi), and then by using Schauder fixed point theory and inverse transform ideas, some new results on the existence and uniqueness of periodic solutions are obtained. The research method is different from the method commonly used in the literature.

关键词

中立型微分方程 / 周期解 / 存在性 / 唯一性 / 不动点理论.

Key words

Neutral differential equations / periodic solutions / existence / uniqueness / fixed point theory.

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陈志彬 , 黄立宏. 一类中立型泛函微分方程周期解的存在性与唯一性. 系统科学与数学, 2011, 31(4): 489-500. https://doi.org/10.12341/jssms10379
CHEN Zhibin , HUANG Lihong. EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A CLASS OFFUNCTIONAL NEUTRAL DIFFERENTIAL EQUATIONS. Journal of Systems Science and Mathematical Sciences, 2011, 31(4): 489-500 https://doi.org/10.12341/jssms10379
中图分类号： 34K15    34C25   
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