On the Regularity of Mild Solutions to Complete Higher Order Differential Equations on Banach Spaces
نویسندگان
چکیده
For the complete higher order differential equation u(t) = Σn−1 k=0Aku (t) + f(t), t ∈ R (*) on a Banach space E, we give a new definition of mild solutions of (*). We then characterize the regular admissibility of a translation invariant subspace M of BUC(R,E) with respect to (*) in terms of solvability of the operator equation Σn−1 j=0AjXD j −XD = C. As application, almost periodicity of mild solutions of (*) is proved. Full text
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