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Abstract and Applied Analysis
Volume 2003, Issue 15, Pages 865-880
http://dx.doi.org/10.1155/S1085337503303057

On the mild solutions of higher-order differential equations in Banach spaces

Department of Mathematics, Western Kentucky University, Bowling Green 42101, KY, USA

Received 28 January 2003

Copyright © 2003 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.

Abstract

For the higher-order abstract differential equation u(n)(t)=Au(t)+f(t), t, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace of BUC(,E) with respect to the above-mentioned equation in terms of solvability of the operator equation AXX𝒟n=C. As applications, periodicity and almost periodicity of mild solutions are also proved.