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

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  • Nguyen Thanh Lan

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.

Suggested Citation

  • Nguyen Thanh Lan, 2003. "On the mild solutions of higher-order differential equations in Banach spaces," Abstract and Applied Analysis, Hindawi, vol. 2003, pages 1-16, January.
    • Handle: RePEc:hin:jnlaaa:924253
    DOI: 10.1155/S1085337503303057
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