Almost automorphic and pseudo-almost automorphic solutions to semilinear evolution equations with nondense domain
type: Item
instance of: scholarly article
title: Almost automorphic and pseudo-almost automorphic solutions to semilinear evolution equations with nondense domain
zbMATH Open document ID: 1203.34095
DOI: 10.1155/2009/298207
author: Bruno de Andrade
author: Claudio Cuevas
published in: Journal of Inequalities and Applications
publication date: 2009-11-03T00:00:00Z
full work available at URL: https://eudml.org/doc/117793
review text: This nice short paper concerns the existence and uniqueness of almost automorphic (in the sense of Bochner) and pseudo almost automorphic (in the sense of Liang et al) solutions of the semilinear evolution equation \[ x'(t)=Ax(t)+f(t,t,x(t)),t\in \mathbb R \] where \(A\) is a linear and not necessarily densely defined operator satisfying the Hille-Yosida condition. Assuming that the function \(f\) is pseudo almost automorphic with respect to the first variable and satisfies some Lipschitz type condition, the authors achieve their aims using Banach's fixed point theorem. An application to a partial differential equation is given. This problem goes back to the reviewer's paper [Semigroup Forum 69, No.~1, 80--86 (2004; Zbl 1077.47058)]. The results generalize several recent works in the topics.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 43A60
zbMATH DE Number: 5624538
zbMATH Keywords: almost auomorphic functions
zbMATH Keywords: pseudo almost auomorphic functions
zbMATH Keywords: semilinear evolution equations
zbMATH Keywords: Hille-Yosida condition
reviewed by: G. M. N'Guérékata
MaRDI profile type: Publication
OpenAlex ID: W2116719103
Wikidata QID: Q59248555
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description: scientific article; zbMATH DE number 5624538