Based on the oscillation of delay differential equations with piecewise constant argument

the relationship between the oscillation of delay differential equations and that of delay differential inequalities was studied.By constructing the function space and defining the map on the space

and using theorem of control convergence

a sufficient and necessary condition for the existence of positive solutions to delay differential equations and that of delay differential inequalities was obtained.And a sufficient condition for oscillation of delay differential equations with piecewise constant argument was obtained.