关于RFDE 的Lipschitz 指数稳定性  

LIPSCHITZ EXPONENTIALLY STABILITY OF RFDE

作　　者：张月莲[1] 

机构地区：[1]常德师范学院数学系,湖南常德415000

出　　处：《常德师范学院学报（自然科学版）》2001年第2期16-20,共5页Journal of Changde Teachers University

摘　　要：针对滞后型泛函微分方程提出了拟一致Lipschitz指数稳定性概念。根据这一稳定性定义中的Lipschitz系数函数与指数函数的不同 ,可以分别包括已有的稳定、一致稳定、渐近稳定、指数渐近稳定等概念。因此 ,拟一致Lipschitz指数稳定又可以认为是上述稳定性的统一形式。一致Lipschitz稳定性也是一种新的稳定性 ,它包括稳定与一致稳定。但对非线性方程它并不被一致渐近稳定所蕴含。重点讨论了在条件 :“函数f(t,)于R+ ×BnH 的任一紧子集R+ ×BnH′(H′≤H)上满足 : f(t,1) -f(t,2 ) ≤E (H′) sup-r≤θ≤ 0 1(θ) -2 (θ) 其中E (H′)≥ 0是仅依赖于H′的常数”下 。The definition of quasi-uniform Lipschitz exponentially stability for retared functional differential equations was established.According to difference between Lipschitz coefficient functions and Lipschitz exponentially functions of the definition,it included stability,uniform stability,asymptolical stability,exponentially asymptolical stability etc.Quasi-uniform Lipschits exponentially stability was considered as unity form of these stabiilty mentioned above.Unity form of these stability which contained stability and uniform stability was also a new stability,but uniform asymptolical stability did not imply nonlinear equations.The sufficient and necessary condition of the stability by applying Liapunor functional was dissussed under the condition:function f(t,) satisfies: ｜f(t, 1) f(t, 2)｜≤E(H′) sup -r≤θ≤0｜ 1(θ)- 2(θ)｜ Where R +×B n H ′ is any compact subest and R +×B n H ′ R +×B n H(H′≤H),EH′ is a nonnegative constant which only depend on the H′ .

关 键 词：泛函微分方程 拟一致Lipschitz指数稳定性 Lipunorv泛函 RFDE Lipschitz泛函方法 

分 类 号：O175.7[理学—数学]