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Volume 2003 (2003), Issue 15, Pages 865-880
doi:10.1155/S1085337503303057

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

Nguyen Thanh Lan

Abstract

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