| 一类三阶非线性微分方程的全局渐近稳定性 |
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| 引用本文： | 邓春红.一类三阶非线性微分方程的全局渐近稳定性[J].吉首大学学报(自然科学版),2009,30(2):26-29. |
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| 作者姓名： | 邓春红 |
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| 作者单位： | (湖南科技学院数学与计算科学系,湖南 永州 425006) |
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| 基金项目： | 永州市科技局资助项目 |
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| 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.
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| 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 |
Global Asymptotic Stability of a Class of Third-Order Nonlinear Differential Equation |
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| DENG Chun-hong.Global Asymptotic Stability of a Class of Third-Order Nonlinear Differential Equation[J].Journal of Jishou University(Natural Science Edition),2009,30(2):26-29. |
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| Authors: | DENG Chun-hong |
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| Institution: | （Department of Mathematics and Computational Science,Hunan Science and Technique College,Yongzhou 425006,Hunan China) |
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| 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. |
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| Keywords: | nonlinear differential equation globally asymptotic stability Lyapunov function energy metric algorithm |
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