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

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.