Oscillations and asymptotic stability of solutions of first order neutral differential equations with piecewise constant argument (Q916863)

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.