Nonuniform Stability of Difference Equations with Infinite Delay

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Abstract: In this note we consider the notion of nonuniform exponential contraction for delay difference equations with infinite delay (one can argue that the only delay difference equations are those with infinite delay, since otherwise we can always bring them to the standard recurrence form in some higher-dimensional space). We consider the general case of a nonautonomous dynamics. Our main objective is to show that exponential contractions persist under sufficiently small linear and nonlinear perturbations. This includes establishing the continuous dependence with the perturbation of the constants in the notion of contraction. We also characterize the nonuniform exponential contractions in terms of strict Lyapunov sequences, in particular by constructing explicitly a strict Lyapunov sequence for each exponential contraction.

Standort
Deutsche Nationalbibliothek Frankfurt am Main
Umfang
Online-Ressource
Sprache
Englisch

Erschienen in
Nonuniform Stability of Difference Equations with Infinite Delay ; volume:10 ; number:1 ; year:2010 ; pages:121-129 ; extent:9
Advanced nonlinear studies ; 10, Heft 1 (2010), 121-129 (gesamt 9)

Urheber

DOI
10.1515/ans-2010-0106
URN
urn:nbn:de:101:1-2405021700188.558839776489
Rechteinformation
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
Letzte Aktualisierung
14.08.2025, 10:48 MESZ

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