Oscillation criteria for a first-order impulsive neutral differential equation of Euler form

In this paper, we are concerned with the oscillation of a first-order impulsive neutral differential equation of Euler form with variable delays. Our results reveal the fact that the oscillatory behavior of all solutions of differential equations without impulses can be inherited by impulsive differential equations under certain impulsive perturbations. It is also seen that the oscillatory properties of all solutions of impulsive differential equations may be caused by the impulsive perturbations, though the corresponding differential equations without impulses admit a nonoscillatory solution. Some examples are also given to illustrate the applicability of the results obtained.