Global stability for separable nonlinear delay differential equations

Consider the following separable nonlinear delay differential equation dy(t)dt=−∑i=0mai(t)gi(y(τi(t))),t≥t0y(t)=φ(t),t≤t0, where we assume that, there is a strictly monotone increasing function f(x) on (−∞, +∞) such that f(0)=0,0