International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2001 / Article

Open Access

Volume 27 |Article ID 371395 | 14 pages | https://doi.org/10.1155/S0161171201012352

On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces

Received11 Mar 2001
Revised04 Jul 2001

Abstract

We consider abstract differential equations of the form u(t)=Au(t)+f(t) or u(t)=Au(t)+f(t) in Banach spaces X, where f(), X is almost-periodic, while A is a linear operator, 𝒟(A)XX. If the solution u() is likewise almost-periodic, X, we establish connections between their Bohr-transforms, uˆ(λ) and fˆ(λ).

Copyright © 2001 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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