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2001 ON STABILITY OF THE EQUAIONS Bu0(t) = Au(t)
Quoc-Phong Vu
Taiwanese J. Math. 5(2): 417-431 (2001). DOI: 10.11650/twjm/1500407347

Abstract

The stability of solutions of the equation $Bu^0(t) = Au(t)$ is considered, where A and B are closed linear operators on a Banach space. Under the well-posedness condition it is proved that if the imaginary part of the spectrum of the pencil (¸B ¡ A) is countable, then a bounded uniformly continuous solution u(t) of the equation is asymptotically almost periodic if and only if the functions e¸ tu(t), (¸ 2 iR), have uniformly convergent means. A condition of exponential stability also is given when the generalized eigenvectors and associated root vectors of the linear pencil (¸B ¡ A) form a Riesz basis.

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Quoc-Phong Vu. "ON STABILITY OF THE EQUAIONS Bu0(t) = Au(t)." Taiwanese J. Math. 5 (2) 417 - 431, 2001. https://doi.org/10.11650/twjm/1500407347

Information

Published: 2001
First available in Project Euclid: 18 July 2017

MathSciNet: MR1832178
Digital Object Identifier: 10.11650/twjm/1500407347

Rights: Copyright © 2001 The Mathematical Society of the Republic of China

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Vol.5 • No. 2 • 2001
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