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On stability in terms of two measures for impulsive systems of functional differential equations. (English) Zbl 1112.34059

The authors consider the following impulsive functional equations
\[ \begin{cases} x'(t)=f(t,x_t), &t\in[t_{k-1},t_k),\\ x(t_k)=J_k(x(t^-_k)), &k=1, 2, \dots,\\ x_{t_0}=\phi. \end{cases} \]
They establish criteria for \((h_0,h)\)-uniform stability, \((h_0,h)\)-equiasymptotic stability, and \((h_0,h)\)-uniform asymptotic stabiliy. The results are illustrated by examples.

MSC:

34K20 Stability theory of functional-differential equations
34K45 Functional-differential equations with impulses
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References:

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