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Zbl 1025.34078
Ivanov, Anatoli; Liz, Eduardo; Trofimchuk, Sergei
Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima. (English)
[J] Tohoku Math. J., II. Ser. 54, No.2, 277-295 (2002). ISSN 0040-8735

The authors present an extension of the well-known 3/2-stability criteria by Yorke for two term functional-differential equations, prove the exact nature of the obtained stability region which coincided with the Yorke result in the special case when the decay term was absent, and establish various sufficient conditions for the global exponential stability of the zero solution to equations like $x'(t)+ax(t)+bf(t,x_t)=0$. In addition, the authors also reveal some interesting links between the following three objects: the Yorke conditions, Halanay inequalities and differential equations with maxima.
[Jinde Cao (Nanjing)]

MSC 2000:: *34K20 Stability theory of functional-differential equations

Keywords: asymptotical stability; functional-differential equations; 3/2-type stability condition; Halanay inequality

Cited in: Zbl 1068.34076 Zbl 1034.34091

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