International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 1, Pages 51-55
doi:10.1155/S0161171287000061

On nth-order differential operators with Bohr-Neugebauer type property

Abstract

Suppose B is a bounded linear operator in a Banach space. If the differential operator dndtn−B 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(n−1),…,u′,u are all almost periodic.