2012
DOI: 10.1016/j.jmaa.2011.06.082
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A version of a theorem of R. Datko for nonuniform exponential contractions

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Cited by 17 publications
(10 citation statements)
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“…The more recent contributions in this line of research deal with certain stochastic extensions (see [14]), weaker forms of (exponential stability) (see [5,10,11,15,24]) and with various relaxations of Datko's condition that still imply the existence of exponential stability (see [22,26]). …”
Section: Introductionmentioning
confidence: 99%
“…The more recent contributions in this line of research deal with certain stochastic extensions (see [14]), weaker forms of (exponential stability) (see [5,10,11,15,24]) and with various relaxations of Datko's condition that still imply the existence of exponential stability (see [22,26]). …”
Section: Introductionmentioning
confidence: 99%
“…The results were extended in 2012, in [24], by Preda et al, who have obtained some R. Datko and Lyapunov-type characterizations for the nonuniform exponential stability and dichotomy of an evolution process with a nonuniform exponential growth. In the same year, Preda et al [25] presented some Perron-type results for the nonuniform exponential dichotomy of an evolution operator.…”
Section: Introductionmentioning
confidence: 83%
“…We emphasize that some previous works did consider the problem of characterizing exponential behavior for the nonautonomous dynamics in terms of the appropriate Lyapunov equation (see [22,[39][40][41] and references therein), but that our results are the first one that deal with the case of exponential trichotomies. This can be regarded as a principal contribution of the present paper since the notion of an exponential trichotomy is the weakest one under which one is still able to obtain certain information about the qualitative behavior of the dynamics.…”
Section: Introductionmentioning
confidence: 99%