Abstract

Suppose B is a bounded linear operator in a Banach space. If the differential operator dndtnB has a Bohr-Neugebauer type property for Bochner almost periodic functions, then, for any Stepanov almost periodic continuous function g(t) and any Stepanov-bounded solution of the differential equation dndtnu(t)Bu(t)=g(t), u(n1),,u,u are all almost periodic.