On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces

Samuel Zaidman

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 27, 1-14

Abstract:

We consider abstract differential equations of the form u ′ ( t ) = A u ( t ) + f ( t ) or u ″ ( t ) = A u ( t ) + f ( t ) in Banach spaces X , where f ( ⋅ ) , ℝ → X is almost-periodic, while A is a linear operator, 𝒟 ( A ) ⊂ X → X . If the solution u ( ⋅ ) is likewise almost-periodic, ℝ → X , we establish connections between their Bohr-transforms, u ˆ ( λ ) and f ˆ ( λ ) .

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:371395

DOI: 10.1155/S0161171201012352

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