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Uniform stability for one-dimensional delay-differential equations with dominant delayed term. (English) Zbl 0706.34065

This work is an extension of the work done earlier by the author and J. Sugie [J. Math. Anal. Appl. 134, No.2, 408-425 (1988; Zbl 0663.34059)]. The author considers delay-differential equation of the form \[ (*)\quad x'(t)=G(t,x(t))+F(t,x_ t), \] where G: \([0,\infty)\times S(H)\to R\) and F: \([0,\infty)\times C^ q(H)\to R\) are continuous, \(S(H)=\{x\in R:| x| <H\}\), \(C^ q(H)=\{\phi \in C^ q:\| \phi \| <H\}\) and \(C^ q\), \(q\geq 0\), is the space of continuous functions on [-q,0] with the usual sup norm. The stability region depending on q has been obtained for (*). Some results concerning the asymptotic stability of the zero solution of (*) are given.
Reviewer: N.Parhi

MSC:

34K20 Stability theory of functional-differential equations

Citations:

Zbl 0663.34059
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References:

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