On delay differential equations with impulses.

*(English)*Zbl 0687.34065The authors’ summary: Sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of
\[
\dot x(t)+ax(t- \tau)=\sum^{\infty}_{j=1}b_ jx(t_ j-\tau)(t-t_ j),\quad t\neq t_ j,
\]
and for the existence of a nonoscillatory solution; conditions are also obtained for all solutions to be oscillatory. The asymptotic behaviour of an impulsively perturbed delay-logistic equation is investigated as an extension to a nonlinear equation.

Reviewer: J.Myjak

##### MSC:

34K20 | Stability theory of functional-differential equations |

##### Keywords:

oscillation; asymptotic stability; nonoscillatory solution; impulsively perturbed delay-logistic equation
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\textit{K. Gopalsamy} and \textit{B. G. Zhang}, J. Math. Anal. Appl. 139, No. 1, 110--122 (1989; Zbl 0687.34065)

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##### References:

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