### Exponential stability for periodic evolution families of bounded linear operators.

Buşe, C. (2001)

Rendiconti del Seminario Matematico

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Buşe, C. (2001)

Rendiconti del Seminario Matematico

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Moukaddem, N. (2001)

Rendiconti del Seminario Matematico

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Phóng Vũ (1999)

Studia Mathematica

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A characterization of exponentially dichotomic and exponentially stable ${C}_{0}$-semigroups in terms of solutions of an operator equation of Lyapunov type is presented. As a corollary a new and shorter proof of van Neerven’s recent characterization of exponential stability in terms of boundedness of convolutions of a semigroup with almost periodic functions is given.

Megan, M., Sasu, L., Sasu, B. (2000)

Acta Mathematica Universitatis Comenianae. New Series

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Mihail Megan, Adina Luminiţa Sasu, Bogdan Sasu (2003)

Archivum Mathematicum

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In this paper we give necessary and sufficient conditions for uniform exponential instability of evolution families in Banach spaces, in terms of Banach function spaces. Versions of some well-known theorems due to Datko, Neerven, Rolewicz and Zabczyk, are obtained for the case of uniform exponential instability of evolution families.

Vũ Phóng (1997)

Banach Center Publications

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This paper is chiefly a survey of results obtained in recent years on the asymptotic behaviour of semigroups of bounded linear operators on a Banach space. From our general point of view, discrete families of operators ${T}^{n}:n=0,1,...$ on a Banach space X (discrete one-parameter semigroups), one-parameter ${C}_{0}$-semigroups $T\left(t\right):t\ge 0$ on X (strongly continuous one-parameter semigroups), are particular cases of representations of topological abelian semigroups. Namely, given a topological abelian semigroup S, a family...

Ungureanu, Viorica Mariela (2004)

Acta Universitatis Apulensis. Mathematics - Informatics

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Cheban, D.N. (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Buşe, Constantin, Jitianu, Oprea (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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deLaubenfels, R., Latushkin, Y. (1995)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Sasu, Adina Luminiţa (2010)

Advances in Difference Equations [electronic only]

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