Almost automorphic solutions to some differential equations in Banach spaces (Q1573706)

Summary: The author discusses the conditions under which bounded solutions to the evolution equation \[ x'(t)= Ax(t)+ f(t) \] in a Banach space are almost automorphic whenever \(f(t)\) is almost automorphic and \(A\) generates a \(C_0\)-group of strongly continuous operators. He also gives a result for asymptotically almost automorphic solutions for the more general case of \[ x'(t)= Ax(t)+ f(t,x(t)). \]