On delay differential equations with impulses. (English) Zbl 0687.34065

The 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


34K20 Stability theory of functional-differential equations
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