一类二阶非线性泛函微分方程的渐近稳定性  

Asymptotic Stability of a Class of Nonlinear Second Order Functional Differential Equation

作　　者：张平正[1] 

机构地区：[1]江苏理工大学理学院,江苏镇江212013

出　　处：《江苏理工大学学报（自然科学版）》2001年第1期89-91,共3页Journal of Jiangsu University of Science and Technology(Natural Science)

基　　金：江苏理工大学青年基金

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。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.

关 键 词：泛涵方程 渐近稳定性 LYAPUNOV泛函 二阶非线性泛涵微分方程 

分 类 号：O177.91[理学—数学]