| 一类二阶非线性泛函微分方程的渐近稳定性 |
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| 引用本文： | 张平正.一类二阶非线性泛函微分方程的渐近稳定性[J].江苏大学学报(自然科学版),2001,22(1):89-91. |
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| 作者姓名： | 张平正 |
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| 作者单位： | 江苏理工大学理学院, |
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| 摘 要： | 利用Lyapunov泛函方法 ,讨论了一类二阶非线性泛函微分方程x″(t) +φ(x′(t) ,t) +f(x(t-r(t) ) ) =0解的渐近稳定性 ,基于｜x′(t) ｜积分的下半有界性 ,得到关于x′(t)的主要引理 ,改进了 φ(x′(t) ,t) /x′(t)积分上界、下界的条件 ,得到了一些新结果 ,推广了方程在线性、非线性、常时滞、变时滞情形下某些相关结论
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| 关 键 词： | 泛函方程 非线性 渐近 稳定性 Lyapunov泛函 |
| 文章编号： | 1007-1741(2001)01-0089-03 |
| 修稿时间： | 2000年6月27日 |
Asymptotic Stability of a Class of Nonlinear Second Order Functional Differential Equation |
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| ZHANG Ping-zheng.Asymptotic Stability of a Class of Nonlinear Second Order Functional Differential Equation[J].Journal of Jiangsu University:Natural Science Edition,2001,22(1):89-91. |
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| Authors: | ZHANG Ping-zheng |
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| Abstract: | By using the method of Lyapunov functional, the asymptotic stability of a class of nonlinear second order functional differential equation x″(t)+φ(x′(t),t)+f(x(t-r(t)))=0 is studied. Based on the lower boundness of the integral of |x′(t)|, a main lemma about x′(t) is obtained. The lower and upper bound of the ingegrals of φ(x′(t), t)/x′(t) are improved. Some new results are obtained. Some related results about the equation of linear, nonlinear, constant delay are generalized. |
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| Keywords: | function equation nonlinearity asymptotic stability lyapunov functih |
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