Weighted pseudo almost automorphic functions and applications to abstract differential equations

Joël Blot (1) , Gisèle Massengo Mophou (2) , Denis Pennequin (1) , Gaston N'Guérékata

1 Marin Mersenne - Pour les Mathématiques, l'Informatique et l'Interdisciplinarité
2 D.M.I. - Département de Mathématiques et Informatique

This paper is concerned with weighted pseudo almost automorphic functions, which are more general and complicated than weighted pseudo almost periodic functions. Using these properties, we establish an existence and uniqueness theorem for pseudo almost automorphic mild solutions to semilinear differential equations in a Banach spaces which extends known results.

Mots clés: almost automorphic; pseudo almost automorphic; composition; weithed pseudo almost automorphic; $C_0$-semigroup of bounded operators; abstract differential equation; mild solution

Domaines: Analyse classique [math.CA]

Joël Blot, Gisèle Massengo Mophou, Denis Pennequin, Gaston N'Guérékata. Weighted pseudo almost automorphic functions and applications to abstract differential equations. Nonlinear Analysis: Theory, Methods and Applications, 2010, 72 (1), pp.430-438. ⟨hal-00617634⟩