Abstract
We prove that the exponential dichotomy of a strongly continuous evolution family on a Banach space is equivalent to the existence and uniqueness of continuous bounded mild solutions of the corresponding inhomogeneous equation. This result addresses nonautonomous abstract Cauchy problems with unbounded coefficients. The technique used involves evolution semigroups. Some applications are given to evolution families on scales of Banach spaces arising in center manifolds theory. © 1998 Plenum Publishing Corporation.
Recommended Citation
Y. Latushkin et al., "Exponential Dichotomy and Mild Solutions of Nonautonomous Equations in Banach Spaces," Journal of Dynamics and Differential Equations, vol. 10, no. 3, pp. 489 - 510, Springer, Jan 1998.
The definitive version is available at https://doi.org/10.1023/A:1022609414870
Department(s)
Mathematics and Statistics
Keywords and Phrases
Central manifolds; Exponential dichotomy; Mild solutions
International Standard Serial Number (ISSN)
1572-9222; 1040-7294
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Springer, All rights reserved.
Publication Date
01 Jan 1998
Comments
National Science Foundation, Grant DMS-9622105