Open Access
2018 On a Bohr-Neugebauer property for some almost automorphic abstract delay equations
Rachid Benkhalti, Brahim Es-sebbar, Khalil Ezzinbi
J. Integral Equations Applications 30(3): 313-345 (2018). DOI: 10.1216/JIE-2018-30-3-313


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.


Download Citation

Rachid Benkhalti. Brahim Es-sebbar. Khalil Ezzinbi. "On a Bohr-Neugebauer property for some almost automorphic abstract delay equations." J. Integral Equations Applications 30 (3) 313 - 345, 2018.


Published: 2018
First available in Project Euclid: 8 November 2018

zbMATH: 06979943
MathSciNet: MR3874004
Digital Object Identifier: 10.1216/JIE-2018-30-3-313

Primary: 34C27 , 35B15 , 35R10

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

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

Vol.30 • No. 3 • 2018
Back to Top