Oscillatory and nonoscillatory delay equations with piecewise constant argument

We introduce a new technique to analyze certain difference equations to obt ain some new type and also "best possible" oscillation and nonoscillation c riteria for the nonautonomous delay differential equation with piecewise co nstant argument of the form y'(t) + a(t)y(t) + b(t)y([t - 1]) = 0, where a( t) and b(t) are continuous functions on [-1, infinity), b(t) greater than o r equal to 0, and [.] denotes the greatest integer function. (C) 2000 Acade mic Press.