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Zbl 0639.34050
Lyubich, Yu.I.; Vu Quôc Phóng
Asymptotic stability of linear differential equations in Banach spaces. (English)
[J] Stud. Math. 88, No.1, 37-42 (1988). ISSN 0039-3223; ISSN 1730-6337/e

Let A be a generator of a strongly continuous bounded semigroup T(t), $t\ge 0$. We prove that if the intersection of the spectrum of A and the imaginary axis is at most countable and $A\sp*$ has no purely imaginary eigenvalues, then the Cauchy problem for the differential equation $\dot x(t)=Ax(t)$, $t\ge 0$, is asymptotically stable.

MSC 2000:: *34D05 Asymptotic stability of ODE
34A30 Linear ODE and systems
34G10 Linear ODE in abstract spaces

Keywords: asymptotic stability; first order differential equations; Cauchy problem

Cited in: Zbl 1004.47027 Zbl 0855.34067 Zbl 0711.47023 Zbl 0652.47022

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