Acta Mathematica Vietnamica
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ON THE ASYMPTOTIC EQUIVALENCE OF LINEAR DELAY EQUATIONS IN BANACH SPACE
DANG DINH CHAUpp. 31-38
Abstract
In this paper we present some sufficient conditions for the asymptotic equivalence of linear evolution equations with time-delay in Banach spaces. Besides, we discuss the asymptotic relationship between $C_0$ groups and strongly continuous evolutionary processes. The obtained results extend the Levinsons theorem on the asymptotic equivalence of linear differential equations.