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

Nguyen Thanh Lan

Abstract and Applied Analysis, 2003, vol. 2003, 1-16

Abstract:

For the higher-order abstract differential equation u ( n ) ( t ) = A u ( 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 A X − X 𝒟 n = C . As applications, periodicity and almost periodicity of mild solutions are also proved.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:924253

DOI: 10.1155/S1085337503303057

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