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Discrete characterizations of exponential dichotomy for evolution families
 Irish. Math. Soc. Bulletin
, 2003
"... Abstract. We present some characterizations of exponential dichotomy using a discrete argument. The results obtained generalize to the case of exponential dichotomy some theorems proved by Littman, Rolewicz and Zabczyk. 1. ..."
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Abstract. We present some characterizations of exponential dichotomy using a discrete argument. The results obtained generalize to the case of exponential dichotomy some theorems proved by Littman, Rolewicz and Zabczyk. 1.
8 On Uniform Exponential Trichotomy of Evolution Operators in Banach Spaces
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On BarreiraValls Polynomial Stability of Evolution Operators in Banach Spaces
"... Our main objective is to consider a concept of nonuniform behavior and obtain appropriate versions of the wellknown stability due to R. Datko and L. Barbashin. This concept has been considered in the works of L. Barreira and C. Valls. Our approach is based on the extension of techniques for exponen ..."
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Our main objective is to consider a concept of nonuniform behavior and obtain appropriate versions of the wellknown stability due to R. Datko and L. Barbashin. This concept has been considered in the works of L. Barreira and C. Valls. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability.
On the dichotomy of evolution families on the halfline: a Lyapunovtype approach.
"... Abstract. Theorems characterizing the exponential dichotomy of evolution families are obtained by proposing a Lyapunovtype operator approach. Thus, are extended classical results due to Coppel [3], Datko [5], DaleckijKrein [4], Massera and Schaffer [8] and also few recent results due to Chicone ..."
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Abstract. Theorems characterizing the exponential dichotomy of evolution families are obtained by proposing a Lyapunovtype operator approach. Thus, are extended classical results due to Coppel [3], Datko [5], DaleckijKrein [4], Massera and Schaffer [8] and also few recent results due to ChiconeLatushkin [2]. 1
Communicated by Dorel Mihet¸
"... Uniform exponential stability for evolution families ..."
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ON THE ASYMPTOTIC BEHAVIOUR OF INDIVIDUAL ELEMENTS UNDER ONEPARAMETER SEMIGROUPS
"... Abstract. Let T = {T (t)}t≥0 be a strongly continuous semigroup of linear operators on the Banach space X. We point out a sufficient condition to guarantee an exponential decay (as t → ∞) of an individual trajectory t 7 → T (t)x0. ..."
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Abstract. Let T = {T (t)}t≥0 be a strongly continuous semigroup of linear operators on the Banach space X. We point out a sufficient condition to guarantee an exponential decay (as t → ∞) of an individual trajectory t 7 → T (t)x0.
C. Chilarescu – A. Pogan – C. Preda ∗ A CHARACTERIZATION OF THE EXPONENTIAL STABILITY OF EVOLUTIONARY PROCESSES IN TERMS OF THE
"... Abstract. A characterization of the exponential stability of evolutionary rocesses in terms of the admissibility of some pairs of spaces, is given. The method of ”test functions ” from a very large class of spaces is used. Thus are obtained generalizations of some results given by N. van Minh, F. Ra ..."
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Abstract. A characterization of the exponential stability of evolutionary rocesses in terms of the admissibility of some pairs of spaces, is given. The method of ”test functions ” from a very large class of spaces is used. Thus are obtained generalizations of some results given by N. van Minh, F. Rabiger and R. Schnaubelt. 1.