On the existence of almost automorphic generalized solutions to some generalized differential equations

Mohamed Elomari; Mohamed Chaib; Said Melliani

doi:10.5269/bspm.63116

Mohamed Elomari Sultan Moulay Sliman University https://orcid.org/0000-0002-4256-1434
Mohamed Chaib Sultan Moulay Sliman University https://orcid.org/0000-0002-9088-0640
Said Melliani Sultan Moulay Sliman University

Abstract

This paper is devoted to study some regularity of almost automorphic and asymptotic almost automorphic generalized solution of the differential equation d dtu(t) = Au(t) + f(t), in the framework of the Colombeau algebras. Under certain assumptions about the second member we showed that the generalized solution is an asmptotically almost automorphic in the sense of genaralized functions.

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