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Distribution of values of linear functions and asymptotic behavior of trajectories of some dynamical systems

โœ Scribed by N. G. Moshchevitin

Publisher
SP MAIK Nauka/Interperiodica
Year
1995
Tongue
English
Weight
587 KB
Volume
58
Category
Article
ISSN
0001-4346

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On the Spectrum, Complete Trajectories,
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โœ V.Q. Phong ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 594 KB

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)\}