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Zbl 0901.34068
Berezansky, L.; Idels, L.
Exponential stability of some scalar impulsive delay differential equations.
(English)
[J] Commun. Appl. Anal. 2, No.3, 301-308 (1998). ISSN 1083-2564

The authors obtain exponential stability results for impulsive delay differential equations $$\dot{x}(t)+ a(t)x(t)+ \sum_{k=1}^m b_k(t) x [h_k(t)]= f(t), \tag 1$$ $$x(\mu_j)= B_j x(\mu_j-0), \qquad j =1,2,\dots, \tag 2$$ where $h_k(t) \le t, t \in [0,\infty)$ and $\lim_{j \to \infty} \mu_j= \infty$. The approach is based on a reduction of the stability of (1), (2) to the solvability of a certain operator equation of second kind [cf. {\it A. Anokhin, L. Berezansky} and {\it E. Braverman}, J. Math. Anal. Appl. 193, No. 3, 923-941 (1995; Zbl 0837.34076)].
[D.Bainov (Sofia)]
MSC 2000:
*34K20 Stability theory of functional-differential equations
34A37 Differential equations with impulses

Keywords: exponential stability; impulsive delay differential equations

Citations: Zbl 0837.34076

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