Exponential dichotomies of linear dynamic equations on measure chains under slowly varying coefficients

Unifying ordinary differential and difference equations, we consider linear dynamic equations on measure chains or time scales, which possess an exponential dichotomy uniformly in a parameter, and show that this dichotomy is robust, if the mentioned parameter changes slowly in time. Here, the equati...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2004, Vol.289 (1), p.317-335
Main Author: Pötzsche, Christian
Format: Article
Language:English
Subjects:
Exact sciences and technology
Exponential dichotomy
Global analysis, analysis on manifolds
Linear dynamic equation
Mathematical analysis
Mathematics
Ordinary differential equations
Sciences and techniques of general use
Slowly varying
Time scale
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:Unifying ordinary differential and difference equations, we consider linear dynamic equations on measure chains or time scales, which possess an exponential dichotomy uniformly in a parameter, and show that this dichotomy is robust, if the mentioned parameter changes slowly in time. Here, the equations can be infinite dimensional and are not assumed to be invertible.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2003.09.063