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Zbl 1084.34066
Wang, Qing; Liu, Xinzhi
Exponential stability for impulsive delay differential equations by Razumikhin method.
(English)
[J] J. Math. Anal. Appl. 309, No. 2, 462-473 (2005). ISSN 0022-247X

This paper deals with the exponential stablity of the solutions of the following impulsive delay differential equation $$\dot x(t)=f(t,x_t), \ \ t\not=t_{k},$$ $$\Delta x(t)=I_{k}(t,x_{t^{-}}), \ t=t_{k}, \ k\in \bbfN,$$ $$x_{t_{0}}=\phi.$$ The proofs are based on the Razumikhin method. Some examples illustrating the results are presented.
[Mouffak Benchohra (Sidi Bel Abbes)]
MSC 2000:
*34K20 Stability theory of functional-differential equations
34K45 Equations with impulses

Keywords: Razumikhin technique; Lyapunov function; impulsive delay differential equation; exponential stability

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