Abstract and Applied Analysis
Volume 2003 (2003), Issue 15, Pages 865-880
doi: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 Nguyen Thanh Lan. 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∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E) with respect to the above-mentioned equation in terms of solvability of the operator equation AX−X𝒟n=C. As applications, periodicity and almost periodicity of mild solutions are also proved.