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Exponential Dichotomy and Eberlein-Weak Almost Periodic Solutions

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DOI: 10.4236/am.2012.39144    2,966 Downloads   4,985 Views

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.

Cite this paper

E. Dads, S. Fatajou and L. Lhachimi, "Exponential Dichotomy and Eberlein-Weak Almost Periodic Solutions," Applied Mathematics, Vol. 3 No. 9, 2012, pp. 969-975. doi: 10.4236/am.2012.39144.

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