Two classes of positive solutions of first order functional differential equations of delayed type

The equation ẏ(t)=−f(t,yt) is considered. The existence of two classes of positive solutions asymptotically different for t→+∞t→+∞ is proved using the retract method. With the aid of solutions of two auxiliary linear equations with several delays, constructed using upper and lower linear functional estimates of the right-hand side of the equation considered, inequalities for both types of positive solutions are given as well.