International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 473-476
doi:10.1155/S0161171289000608

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

Abstract

We consider a differential equation ddtu(t)-Bu(t)=f(t), where the functions u and f map the real line into a Banach space X and B: X →X is a bounded linear operator. Assuming that any Stepanov-bounded solution u is Stepanov almost-periodic when f is Bochner almost-periodic, we establish that any Stepanov-bounded solution u is Bochner almost-periodic when f is Stepanov almost-periodic. Some examples are given in which the operator ddt-B is shown to satisfy our assumption.