Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line

Let u be a bounded, uniformly continuous, mild solution of an inhomogeneous Cauchy problem on R+: u′(t) = Au(t) + (Latin small letter o with stroke)(t) (t ≥ 0). Suppose that u has uniformly convergent means, σ(A) ∩ i R is countable, and (Latin small letter o with stroke) is asymptotically almost per...