Exponential Dichotomy and Eberlein-Weak Almost Periodic Solutions

Elhadi Ait Dads, Samir Fatajou, Lahcen Lhachimi

Départment de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, Marrakesh, Morocco.
Laboratoire L. M. C.; Départment de Mathématiques et Informatique, Faculté Polydisciplinaire-Safi (FPS)Université Cadi Ayyad, Safi, Morocco.

DOI: 10.4236/am.2012.39144                

Abstract

We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) _{t ∈□} is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.

Keywords

Bounded Solutions; Almost Periodic and Eberlein Weak Almost Periodic Functions; Exponential Dichotomy; Linear Differential Equations

Conflicts of Interest

The authors declare no conflicts of interest.

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