Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima

Abstract

We present an extension of the well-known $3/2$-stability criterion by Yorke for two term functional differential equations. We prove the exact nature of the obtained stability region which coincides with the Yorke result in the special case when the decay term is absent. Moreover, we reveal some interesting links existing between the Yorke conditions, Halanay inequalities and differential equations with maxima, all of them essentially involving the maximum functionals.