Almost automorphic solutions of some differential equations in Banach spaces

Gaston Mandata N'Guerekata

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-5

Abstract:

We discuss the conditions under which bounded solutions of the evolution equation x ′ ( t ) = A x ( t ) + f ( t ) in a Banach space are almost automorphic whenever f ( t ) is almost automorphic and A generates a C 0 -group of strongly continuous operators. We also give a result for asymptotically almost automorphic solutions for the more general case of x ′ ( t ) = A x ( t ) + f ( t , x ( t ) ) .

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:482560

DOI: 10.1155/S0161171200001988

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