Positive and oscillating solutions of differential equations with delay in critical case

This article is devoted to the problem of existence of positive solution for common classes of nonlinear retarded functional differential equations. Some criteria of its existence are proved, as well as some comparison results. The obtained results are applied to the linear case. Moreover, the existence of positive and oscillating solutions of a differential equation with delay ẋ(t)=−a(t)x(t−τ) in the critical case is considered. Some comparisons with known results are given.