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On nonuniform dichotomy for stochastic skew-evolution semiflows in Hilbert spaces

Diana StoicaMihail Megan — 2012

Czechoslovak Mathematical Journal

In this paper we study a general concept of nonuniform exponential dichotomy in mean square for stochastic skew-evolution semiflows in Hilbert spaces. We obtain a variant for the stochastic case of some well-known results, of the deterministic case, due to R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3(1972), 428–445. Our approach is based on the extension of some techniques used in the deterministic case for the study of asymptotic behavior...

Stabilizability and controllability of systems associated to linear skew-product semiflows.

Mihail MeganAdina Luminita SasuBogdan Sasu — 2002

Revista Matemática Complutense

This paper is concerned with systems with control whose state evolution is described by linear skew-product semiflows. The connection between uniform exponential stability of a linear skew-product semiflow and the stabilizability of the associated system is presented. The relationship between the concepts of exact controllability and complete stabilizability of general control systems is studied. Some results due to Clark, Latushkin, Montgomery-Smith, Randolph, Megan, Zabczyk and Przyluski are generalized....

Exponential expansiveness and complete admissibility for evolution families

Mihail MeganBogdan SasuAdina Luminiţa Sasu — 2004

Czechoslovak Mathematical Journal

Connections between uniform exponential expansiveness and complete admissibility of the pair ( c 0 ( , X ) , c 0 ( , X ) ) are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.

Exponential stability and exponential instability for linear skew-product flows

Mihail MeganAdina Luminiţa SasuBogdan Sasu — 2004

Mathematica Bohemica

We give characterizations for uniform exponential stability and uniform exponential instability of linear skew-product flows in terms of Banach sequence spaces and Banach function spaces, respectively. We present a unified approach for uniform exponential stability and uniform exponential instability of linear skew-product flows, extending some stability theorems due to Neerven, Datko, Zabczyk and Rolewicz.

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