Tohoku Mathematical Journal
2002
June
SECOND SERIES VOL. 54, NO. 2

Tohoku Math. J.
54 (2002), 277-295

Title HALANAY INEQUALITY, YORKE 3/2 STABILITY CRITERION, AND DIFFERENTIAL EQUATIONS WITH MAXIMA

Author Anatoli Ivanov, Eduardo Liz and Sergei Trofimchuk

(Received June 19, 2000, revised January 29, 2001)
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.

2000 Mathematics Subject Classification. Primary 34K20.
Key words and phrases. Functional differential equations, asymptotical stability, 3/2-type stability conditions.

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