We present a variation-of-constants formula for functional differential equations of the form $$\dot{y}=ℒ\left(t\right)y_t+f(y_t,t),y_{t_0}=\varphi ,$$ where $ℒ$ is a bounded linear operator and $\varphi$ is a regulated function. Unlike the result by G. Shanholt (1972), where the functions involved are continuous, the novelty here is that the application $t\mapsto f(y_t,t)$ is Kurzweil integrable with $t$ in an interval of $ℝ$, for each regulated function $y$. This means that $t\mapsto f(y_t,t)$ may admit not only many discontinuities, but it can also be highly oscillating and yet, we are able to obtain...

A class of nonlinear neutral differential equations with variable coefficients and delays is considered. Conditions for the existence of eventually positive solutions are obtained which extend some of the criteria existing in the literature. In particular, a linearized comparison theorem is obtained which establishes a connection between our nonlinear equations and a class of linear neutral equations with constant coefficients.