数学物理学报 ›› 2005, Vol. 25 ›› Issue (5): 593-603.

• 论文 •    下一篇

具无限时滞中立型泛函微分方程解的稳定性与有界性

 迪申加卜, 范猛, 王克   

  1. 武警学院基础部,廊坊,东北师范大学数学系,植被生态教育部重点实验室
  • 出版日期:2005-10-25 发布日期:2005-10-25
  • 基金资助:

    国家自然科学基金(10171010)和教育部科学技术重点项目(01061)资助

Stability and Boundedness of Neutral Functional Differential Equations with Infinite Delay

 DI Shen-Jia-Bo, FAN Meng, WANG Ke   

  • Online:2005-10-25 Published:2005-10-25
  • Supported by:

    国家自然科学基金(10171010)和教育部科学技术重点项目(01061)资助

摘要:

以相空间为基础,研究了具有无限时滞中立型泛函微分方程解的稳定性和有界性,建立了方程解为一致稳定,一致渐近稳定的充要性判据;证明了当方程右端泛函满足Lipschitz条件时,解的一致渐近稳定性蕴涵了有界解的存在性,推广了文献[4-6]中已有的相关结果.

关键词: 中立型微分方程, 无限时滞, 稳定性, 有界性, 充要条件.

Abstract:

With the help of the phase space sufficient and necessary criterias are established for the uniform stability and uniformly asymptotic stability of solutions to neutral functional differential equations with infinite delay. In addition, the author also prove that the uniformly asymptotic stability of solutonsimplies the existence of the bounded solutions when the equation satisfies Lipschitz assumption.

Key words: Neutral differential equations, Infinite delay, Stability, Boundedness, Necessary and sufficient conditions

中图分类号: 

  • 34C25,34K20