On weak-almost periodic mild solutions of some linear abstract differential equations

Gaston N'Guerekata

doi:10.3934/proc.2003.2003.672

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2003, Volume 2003: 672-677. Doi: 10.3934/proc.2003.2003.672 open access

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On weak-almost periodic mild solutions of some linear abstract differential equations

Gaston N'Guerekata^1,

1.
Department of Mathematics, Morgan State University, Baltimore, Maryland 21251

Received: June 30, 2002

Revised: March 31, 2003

Published: March 2003

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Abstract

We are concerned with the differential equation $x'(t) = Ax(t) + f(t)$ with a linear operator $A$ acting in a Banach space $X$ and $f : \mathbb(R) \to X$ a almost periodic function (in Bochner’s sense). We give necessary conditions to ensure that the so-called optimal mild solutions are also weakly almost periodic.

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Mathematics Subject Classification: Primary: 34C27, 35B15; Secondary: 34G10.

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