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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Asymptotic stability in functional-differential equations by Liapunov functionals

Author: Bo Zhang
Journal: Trans. Amer. Math. Soc. 347 (1995), 1375-1382
MSC: Primary 34K20
MathSciNet review: 1264834
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Abstract: We consider the asymptotic stability in a system of functional differential equations $ x'(t) = F(t,{x_t})$ by Liapunov functionals $ V$. The work generalizes some well-known results in the literature in that we only require the derivative of $ V$ to be negative definite on a sequence of intervals $ {I_n} = [{S_n},{t_n}]$. We also show that it is not necessary to require a uniform upper bound on $ V$ for nonuniform asymptotic stability.

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Keywords: Functional differential equations, Liapunov functionals, asymptotic stability
Article copyright: © Copyright 1995 American Mathematical Society