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Stability and oscillation in delay differential equations with piecewise constant arguments. (English) Zbl 0729.34056

The authors consider a first order nonlinear delay differential equation with piecewise constant arguments and obtain results on the asymptotic behaviour of solutions of the equation. Razumikhin type methods are employed to study the stability of the zero solution of the equation. The results are illustrated by appropriate examples.

MSC:

34K20 Stability theory of functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
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