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Zbl 0894.34064
Gy\" ori, I.; Pituk, M.
Stability criteria for linear delay differential equations. (English)
[J] Differ. Integral Equ. 10, No.5, 841-852 (1997). ISSN 0893-4983

Linear delay differential systems of the form $$ \dot x(t)= A(t)x(t-\tau (t)) $$ with a continuous $n\times n$-matrix-valued function $A$ defined on $[t_0, \infty)$ and with a continuous $\tau : [t_0, \infty) \mapsto [0,r]$, $0 < r =\text {const}$ are considered. \par Conditions for the stability and asymptotic stability of the zero solution of the given equation are presented. The results are used for discussing the equation $\dot x(t)= \dfrac {\sin t}{t^{\alpha }}x(t- r)$ in dependence on the parameter $\alpha $.
[Š.Schwabik (Praha)]

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

Keywords: stability; asymptotic stability; linear delay differential systems

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Zentralblatt MATH Berlin [Germany]