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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 |

### Keywords:

characteristic equation; scalar delay differential equation with piecewise constant argument
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\textit{A. R. Aftabizadeh} et al., Proc. Am. Math. Soc. 99, 673--679 (1987; Zbl 0631.34078)

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### References:

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