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Oscillations and asymptotic stability of solutions of first order neutral differential equations with piecewise constant argument. (English) Zbl 0704.34078

The author considers the first order neutral differential equation \[ d/dt(y(t)+py(t+))=qy([t+]), \] where [\(\cdot]\) denotes the greatest integer function. Because of the piecewise constant argument at the right-hand-side, the equation is alternately of delayed and advanced type. The author gives some results about both the oscillatory behavior of solutions and the asymptotic stability of the zero solution.
Reviewer: A.Bacciotti

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K20 Stability theory of functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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References:

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