Journal of Integral Equations and Applications

On a Bohr-Neugebauer property for some almost automorphic abstract delay equations

Rachid Benkhalti, Brahim Es-sebbar, and Khalil Ezzinbi

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Abstract

This paper is a continuation of the investigations done in the literature regarding the so called Bohr-Neugebauer property for almost periodic differential equations in Hilbert spaces. The aim of this work is to extend the investigation of this property to almost automorphic functional partial differential equations in Banach spaces. We use a compactness assumption which turns out to relax assumptions made in some earlier works for differential equations in Hilbert spaces. Two new integration theorems for almost automorphic functions are proven in the process. To illustrate our main results, we propose an application to a reaction-diffusion equation with continuous delay.

Article information

Source
J. Integral Equations Applications, Volume 30, Number 3 (2018), 313-345.

Dates
First available in Project Euclid: 8 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1541668116

Digital Object Identifier
doi:10.1216/JIE-2018-30-3-313

Mathematical Reviews number (MathSciNet)
MR3874004

Zentralblatt MATH identifier
06979943

Subjects
Primary: 34C27: Almost and pseudo-almost periodic solutions 35B15: Almost and pseudo-almost periodic solutions 35R10: Partial functional-differential equations

Keywords
Bohr-Neugebauer property almost automorphic solutions semigroup partial functional differential equations

Citation

Benkhalti, Rachid; Es-sebbar, Brahim; Ezzinbi, Khalil. On a Bohr-Neugebauer property for some almost automorphic abstract delay equations. J. Integral Equations Applications 30 (2018), no. 3, 313--345. doi:10.1216/JIE-2018-30-3-313. https://projecteuclid.org/euclid.jiea/1541668116


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