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Zbl 0631.34078
Aftabizadeh, A.R.; Wiener, Joseph; Xu, Jian-Ming
Oscillatory and periodic solutions of delay differential equations with piecewise constant argument. (English)
[J] Proc. Am. Math. Soc. 99, 673-679 (1987). ISSN 0002-9939; ISSN 1088-6826/e

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.
[H.Engler]

MSC 2000:: *34K99 Functional-differential equations
34C25 Periodic solutions of ODE
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
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

Cited in: Zbl 0848.34061

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