On exponential stability of a linear delay differential equation with an oscillating coefficient

New explicit exponential stability conditions are obtained for the nonautonomous linear equation ẋ(t)+a(t)x(h(t))=0, where h(t)≤th(t)≤t and a(t)a(t) is an oscillating function.We apply the comparison method based on the Bohl–Perron type theorem. Coefficients and delays are not assumed to be continuous.Some real-world applications and several examples are also discussed.