a Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, BP 2390 Marrakech, Morocco b Department of Mathematics, Morgan State University, 1700 East Cold Spring Lane, Baltimore, MD 21251, USA
Abstract:
In this work, we study the existence of almost automorphic solutions for some partial functional differential equations. We prove that the existence of a bounded solution on R+ implies the existence of an almost automorphic solution. Our results extend the classical known theorem by Bohr and Neugebauer on the existence of almost periodic solutions for inhomegeneous linear almost periodic differential equations. We give some applications to hyperbolic equations and Lotka-Volterra type equations used to describe the evolution of a single diffusive animal species.