李雅普诺夫函数与中立型泛函微分方程的稳定性

Ｒａｚｕｍｉｋｈｉｎ技巧已有效地用于各种具有限限或无限时滞的滞后型泛函微分方程，而对于中立型泛函微分方程却不即么成功。本文将推广Ｒａｚｕｍｉｋｈｉｎ技巧到具有无穷时滞的中立型泛函微分方程ｘ＝ｆ（ｔ，ｘｔ，ｘｔ）。甚至此，我们了中立积分微分方程渐近稳定性的充分条件。

LIAPUNOV FUNCTIONS AND STABILITY IN NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Razumikhin technique has been used very effectively on various type ofretarded functional differential equations with finite or infinite delays. It has not, however, been used with much success on neutral functional differential equations (NFDE).Our paper will generalize the Razumikhin technique to a NFDE x(t)= f(t,x,,x) withinfinite delays. Based on the technique, we deduce sufficient conditions for asymptoticstability of neutral integro-differential equations. The advantage of our methods is allowing the functiolls f to be unbounded. However, most classical results require that f bebounded for xt and xt bounded to obtain stability properties.