Almost automorphic solutions for some nonautonomous evolution equations under the light of integrable dichotomy

Abdoul Aziz Kalifa Dianda; Khalil Ezzinbi

doi:10.56754/0719-0646.2701.029

DOI:

https://doi.org/10.56754/0719-0646.2701.029

Abstract

In this work, we prove the existence and uniqueness of \(\mu\)-pseudo almost automorphic solutions for a class of semilinear nonautonomous evolution equations of the form: \(u'(t)=A(t)u(t)+f(t,u(t)),\; t\in\mathbb{R}\) where \((A(t))_{t\in \mathbb{R}}\) is a family of closed linear operators acting in a Banach space \( X \) that generates an evolution family having an integrable dichotomy on \( \mathbb{R} \) and \( f : \mathbb{R} \times X \to X \) is \( \mu \)-pseudo almost automorphic with respect to \(t\) and Lipshitzian in the second variable. Moreover we provide an application illustrating our results.

Keywords

Evolution family , delay evolution equations , exponential dichotomy , integrable dichotomy , µ-pseudo almost automorphic functions

Mathematics Subject Classification:

46T20 , 47J35 , 34C27 , 35K58

Abdoul Aziz Kalifa Dianda Department of Mathematics, Faculty of Sciences and Technologies, Norbert Zongo University, Koudougou A.B.P. 376, Burkina Faso. https://orcid.org/0009-0003-5894-8582
Khalil Ezzinbi Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh B.P. 2390-40000, Morocco. https://orcid.org/0000-0001-5334-2264

Pages: 29–54
Date Published: 2025-04-27
Vol. 27 No. 1 (2025)

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