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Oscillatory and periodic solutions of delay differential equations with piecewise constant argument. (English) Zbl 0631.34078

The authors give sufficient conditions for all solutions of the scalar delay differential equation with piecewise constant argument \[ y'(t)+a(t)y(t)+b(t)y([t-1])=0 \] to be oscillatory. In the case of constant coefficients, these conditions are shown to be also necessary, the asymptotic stability of the zero solution is studied, and periodic solutions are characterized.
Reviewer: H.Engler

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C25 Periodic solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34K10 Boundary value problems for functional-differential equations
34K20 Stability theory of functional-differential equations
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