TITLE:
Exponential Dichotomy and Eberlein-Weak Almost Periodic Solutions
AUTHORS:
Elhadi Ait Dads, Samir Fatajou, Lahcen Lhachimi
KEYWORDS:
Bounded Solutions; Almost Periodic and Eberlein Weak Almost Periodic Functions; Exponential Dichotomy; Linear Differential Equations
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.9,
September
27,
2012
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.