Oscillatory and Nonoscillatory Delay Equations with Piecewise Constant Argument1

We introduce a new technique to analyze certain difference equations to obtain some new type and also ‘‘best possible’’ oscillation and nonoscillation criteria for the nonautonomous delay differential equation with piecewise constant argument of the form y Žt. aŽt.yŽt. bŽt.yŽ t 1 . 0, where aŽt. and bŽt. are continu- ous functions on 1, ., bŽt. 0, and denotes the greatest integer function.