International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1989 / Article

Open Access

Volume 12 |Article ID 703279 | 4 pages | https://doi.org/10.1155/S0161171289000608

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

Received01 Jan 1987
Revised20 Apr 1987

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.

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.

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