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

Abstract

For the higher-order abstract differential equationwe give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ᏹ of BUC(R,E) with respect to the above-mentioned equation in terms of solvability of the operator equation AX − XᏰ n = C. As applications, periodicity and almost periodicity of mild solutions are also proved.