Tohoku Mathematical Journal

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

Anatoli Ivanov, Eduardo Liz, and Sergei Trofimchuk

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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.

Article information

Source
Tohoku Math. J. (2), Volume 54, Number 2 (2002), 277-295.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113247567

Digital Object Identifier
doi:10.2748/tmj/1113247567

Mathematical Reviews number (MathSciNet)
MR1904953

Zentralblatt MATH identifier
1025.34078

Subjects
Primary: 34K20: Stability theory

Citation

Ivanov, Anatoli; Liz, Eduardo; Trofimchuk, Sergei. Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima. Tohoku Math. J. (2) 54 (2002), no. 2, 277--295. doi:10.2748/tmj/1113247567. https://projecteuclid.org/euclid.tmj/1113247567


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References

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Tohoku University, Mathematical Institute

Tohoku Mathematical Journal

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