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Rebenda, Josef; Šmarda, Zdeněk

Stability of a functional differential system with a finite number of delays. (English) Zbl 1470.34200

Abstr. Appl. Anal. 2013, Article ID 853134, 10 p. (2013).
Summary: The paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied.

Cited in 1 Document

MSC:

34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
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\textit{J. Rebenda} and \textit{Z. Šmarda}, Abstr. Appl. Anal. 2013, Article ID 853134, 10 p. (2013; Zbl 1470.34200)
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