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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 Hindawi Publishing Corporation. 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 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.