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March  2003, 9(2): 309-321. doi: 10.3934/dcds.2003.9.309

Wright type delay differential equations with negative Schwarzian

Eduardo Liz 1, , Manuel Pinto 2, , Gonzalo Robledo 2, , Sergei Trofimchuk 2, and  Victor Tkachenko 3,

1. 

Departamento de Matemática Aplicada II, E.T.S.I. Telecomunicación, Universidad de Vigo, Campus Marcosende, 36280 Vigo, Spain
2. 

Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile, Chile, Chile
3. 

Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs'ka str. 3, Kiev, Ukraine

Received  August 2001 Revised  May 2002 Published  December 2002

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 $f'(0)<0$ satisfying the standard negative feedback and below boundedness conditions and having everywhere negative Schwarz derivative.
Keywords: Schwarz derivative, global stability, delay differential equations., Wright conjecture, 3/2 stability condition.
Mathematics Subject Classification: 34K2.
Citation: Eduardo Liz, Manuel Pinto, Gonzalo Robledo, Sergei Trofimchuk, Victor Tkachenko. Wright type delay differential equations with negative Schwarzian. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 309-321. doi: 10.3934/dcds.2003.9.309
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