Wright type delay differential equations with negative Schwarzian

Eduardo Liz; Manuel Pinto; Gonzalo Robledo; Sergei Trofimchuk; Victor Tkachenko

doi:10.3934/dcds.2003.9.309

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2003, Volume 9, Issue 2: 309-321. Doi: 10.3934/dcds.2003.9.309

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Wright type delay differential equations with negative Schwarzian

1.
Departamento de Matemática Aplicada II, E.T.S.I. Telecomunicación, Universidad de Vigo, Campus Marcosende, 36280 Vigo
2.
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago
3.
Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs'ka str. 3, Kiev

Received: July 31, 2001

Revised: April 30, 2002

Published: February 2003

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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 $f'(0)<0$ satisfying the standard negative feedback and below boundedness conditions and having everywhere negative Schwarz derivative.

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Mathematics Subject Classification: 34K20.

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