Wright type delay differential equations with negative Schwarzian

Abstract

We prove that the well-known 3/2 stability condition established for the Wright equation (WE) still holds if the nonlinearity $p(\exp (-x)-1)$ in WE is replaced by a decreasing or unimodal smooth function f with $f^{\prime }(0)<0$ satisfying the standard negative feedback and below boundedness conditions and having everywhere negative Schwarz derivative.

12 pages, 1 figure. Some references and comments added to the previous version. Accepted for publication in Discrete and continuous Dynamical Systems