Article ID Journal Published Year Pages File Type
5774725 Journal of Mathematical Analysis and Applications 2017 20 Pages PDF
Abstract
This work continues the investigations done in the literature about the so called Bohr-Neugebauer property for almost periodic differential equations in Hilbert spaces. We give a new sufficient condition to ensure that an almost periodic linear evolution equation in a Banach space has the Bohr-Neugebauer property. More specifically, we investigate when all the bounded solutions on R are almost periodic. This new sufficient condition involves the essential growth bound of the C0-semigroup generated by the autonomous part of the equation. This enables us to investigate the Bohr-Neugebauer property for partial differential equations with solutions living in purely Banach spaces. An application to a size-structured population model will be studied using the theory of positive C0-semigroups.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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