Admissibility criteria for nonuniform dichotomic behavior of nonautonomous systems on the whole line

Adina Luminiţa Sasu and Bogdan Sasu

Applied Mathematics and Computation, 2020, vol. 378, issue C

Abstract: We give new criteria for nonuniform dichotomy of nonautonomous systems on the whole line in terms of admissibility relative to an integral equation. In our approach the input space I(R,X) is an intersection of spaces that can be successively minimized and the output space C(R,X) can be one of some well-known spaces of continuous functions. Using computational arguments, we show that the admissibility of (C(R,X),I(R,X)) leads to a nonuniform exponential dichotomy. We expose a complete analysis of the connections between admissibility and nonuniform dichotomy on the whole line and we also discuss several interesting consequences. Moreover, we obtain the explicit expression of the growth rates for dichotomy in terms of the initial exponential growth and the norm of the input-output operator. Finally, we present a direct application of the main result in the case of evolution families which admit uniform exponential growth.

Keywords: Exponential dichotomy; Admissibility; Evolution family; Integral equation (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:378:y:2020:i:c:s0096300320301363

DOI: 10.1016/j.amc.2020.125167

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