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Exponential stability for impulsive delay differential equations by Razumikhin method. (English) Zbl 1084.34066
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.

34K20Stability theory of functional-differential equations
34K45Functional-differential equations with impulses
Full Text: DOI
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