On the existence of C (n) -almost automorphic mild solutions of certain differential equations in Banach spaces - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Communications in Contemporary Mathematics Année : 2020

On the existence of C (n) -almost automorphic mild solutions of certain differential equations in Banach spaces

Résumé

In this paper we study the existence and uniqueness of almost automorphic mild solutions to the semilinear equation u (t) = A(t)u(t) + f (t, u(t)), t ∈ R where A(t) satisfies the Acquistapace-Terreni conditions and generates an exponentially stable family of operators (U (t, s) t≥s and f (t, u) is almost automorphic in t ∈ R for any u ∈ X. This extends a well-known result by G.M. N'Guérékata in the case where A(t) = A does not depend on t. We also investigate the existence of mild C n-almost automorphic solutions of the linear version of the above equation when A is an operator of simplest type.
Fichier principal
Vignette du fichier
Gaston-Gisele-Limbe.pdf (315.58 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02547996 , version 1 (20-04-2020)

Identifiants

  • HAL Id : hal-02547996 , version 1

Citer

Gaston M N'Guérékata, Gisèle Mophou. On the existence of C (n) -almost automorphic mild solutions of certain differential equations in Banach spaces. Communications in Contemporary Mathematics, In press. ⟨hal-02547996⟩

Collections

UNIV-AG LAMIA
56 Consultations
42 Téléchargements

Partager

Gmail Facebook X LinkedIn More