一类三阶非线性微分方程的全局渐近稳定性

journal6 ›› 2009, Vol. 30 ›› Issue (2): 26-29.

一类三阶非线性微分方程的全局渐近稳定性

(湖南科技学院数学与计算科学系,湖南永州 425006)

出版日期:2009-03-25 发布日期:2012-04-25
作者简介:邓春红(1979-),女，湖南永州人,湖南科技学院数学与计算科学系讲师，硕士，主要从事微分方程的稳定性、周期解、概周期解研究.
基金资助:
永州市科技局资助项目

Global Asymptotic Stability of a Class of Third-Order Nonlinear Differential Equation

（Department of Mathematics and Computational Science,Hunan Science and Technique College,Yongzhou 425006,Hunan China)

Online:2009-03-25 Published:2012-04-25

摘要/Abstract

摘要：对一类三阶非线性微分方程利用能量度量法构造了较好的Lyapunov函数,得到其零解全局渐近稳定的一组充分条件,而且去掉了一般要求Lyapunov函数具有无穷大这个较强的条件,只要求系统正半轨有界,所得结果包含并改进了旧的结果.

关键词： 非线性微分方程, 全局渐近稳定性, Lyapunov函数, 能量度量算法

Abstract: A better Lyapunov function of a class of third-order nonlinear differential equations has been constructed by the method of the energy metric algorithm,and some sufficient conditions of globally asympotic stability of zero solution are obtained.The hard condition that Lyapunov function shoud be infinite has been removed,and the only requirement is that the positive orbit of the equation should be bounded.The result not only covers but also improves some of the old results.

Key words: nonlinear differential equation, globally asymptotic stability, Lyapunov function, energy metric algorithm

邓春红. 一类三阶非线性微分方程的全局渐近稳定性[J]. journal6, 2009, 30(2): 26-29.

DENG Chun-Hong. Global Asymptotic Stability of a Class of Third-Order Nonlinear Differential Equation[J]. journal6, 2009, 30(2): 26-29.

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