Yorke and Wright 3/2-stability theorems from a unified point of view

Eduardo Liz; Victor Tkachenko; Sergei Trofimchuk

doi:10.3934/proc.2003.2003.580

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2003, Volume 2003: 580-589. Doi: 10.3934/proc.2003.2003.580 open access

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Yorke and Wright 3/2-stability theorems from a unified point of view

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

Received: August 31, 2002

Revised: February 28, 2003

Published: March 2003

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Abstract

We consider a family of scalar delay differential equations $x'(t) = f(t, x_t)$, with a nonlinearity $f$ satisfying a negative feedback condition combined with a boundedness condition. We present a global stability criterion for this family, which in particular unifies the celebrated 3/2-conditions given for the Yorke and the Wright type equations. We illustrate our results with some applications.

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Mathematics Subject Classification: 34K20.

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