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On an extension of the concept of orbital stability for trajectories of a dynamical system

โœ Scribed by O. V. Druzhinina; A. A. Shestakov

Book ID
110126817
Publisher
SP MAIK Nauka/Interperiodica
Year
2001
Tongue
English
Weight
60 KB
Volume
46
Category
Article
ISSN
1028-3358

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Let \(\{T(t)\}_{1 \geqslant 0}\) be a \(C_{0}\)-semigroup in a Banach space \(X\) with generator \(A\). We prove that if \(\{T(t)\}_{t \geqslant 0}\) is bounded and sun-reflexive, and the sun-dual semigroup is not asymptotically stable, then there exist bounded complete trajectories under \(\{T(t)\}