International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 473-476
On first-order differential operators with Bohr-Neugebauer type property
Department of Mathenmtics, Conoordia Univ., Montreal H3G IM8, P.Quebec, Canada
Received 1 January 1987; Revised 20 April 1987
Copyright © 1989 Aribindi Satyanarayan Rao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider a differential equation u(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 -B is shown to satisfy our assumption.