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Exponential Dichotomies in Intermediate Spaces with Applications to a Diffusively Perturbed Predator-Prey Model

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
108
Issue
1
Identifiers
DOI: 10.1006/jdeq.1994.1024

Abstract

Abstract Intermediate spaces are useful for obtaining maximal regularity when studying reaction-diffusion equations. We give a definition of exponential dichotomies in these spaces. Roughness of the exponential dichotomies and other basic properties are also proved. We then use these notions to investigate the stability of a periodic orbit in a predator-prey model studied by Conway and Smoller when diffusion terms are added.

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