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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) = Au(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 AX − X𝒟n = C. As applications, periodicity and almost periodicity of mild solutions are also proved.

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Handle: RePEc:wly:jnlaaa:v:2003:y:2003:i:15:p:865-880
DOI: 10.1155/S1085337503303057
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