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Stability for impulsive delay differential equations. (English) Zbl 1082.34069
Summary: The stability for the scalar impulsive delay differential equation \[ y'(t)+ a(t)y(t)+F(t,y(\cdot))=0,\quad t\geq 0,\;t\neq\tau_k, \] \[ y(\tau_k^+)-y(\tau_k)= I_k\bigl(y(\tau_k)\bigr),\;k=1,2,\dots,\lim_{k \to\infty}\tau_k=\infty, \] where delay arguments may be bounded or unbounded, is investigated. Some new stability theorems are established which improve and extend several known results in the literature.

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