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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the propagators of second order linear differential equations in Hilbert spaces


Authors: Tijun Xio and Jin Liang
Journal: Proc. Amer. Math. Soc. 113 (1991), 663-667
MSC: Primary 47D09; Secondary 34G10, 34K30, 35R20
MathSciNet review: 1072350
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Abstract: The paper is concerned with the growth properties at infinity of the propagators $ C( \cdot ),S( \cdot )$ of the equation $ u''(t) + Bu'(t) + Au(t) = 0$, where $ A,B$ are densely defined closed linear operators in a Hilbert space. We define $ {\omega _0}(A,B) = \max \{ {\overline {\lim } _{t \to \infty }}{t^{ - 1}}\ln \... ...erline {\lim } _{t \to \infty }}{t^{ - 1}}\ln \left\Vert {S'(t)} \right\Vert\} $, and give a criterion to judge whether $ {\omega _0}(A,B) \leq b$ for a fixed $ b \in R$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1072350-4
PII: S 0002-9939(1991)1072350-4
Keywords: Second order differential equation, propagators, growth property
Article copyright: © Copyright 1991 American Mathematical Society