Regular Article
Unbounded Perturbation of the Exponential Dichotomy for Evolution Equations

https://doi.org/10.1006/jdeq.1996.0125Get rights and content
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Abstract

In this paper we prove that the exponential dichotomy for evolution equations in Banach spaces is not destroyed, if we perturb the equation by “small” unbounded linear operator. This is done by employing a skew-product semiflow technique and a perturbation principle from linear operator theory. Finally, we apply these results to partial parabolic equations and functional differential equations.

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This research was partially supported by NSF-DMS-9306265.