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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

x ˙(t)+ax(t-τ)= j=1 b j x(t j -τ)(t-t j ),tt 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:
34K20Stability theory of functional-differential equations