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

Pages: 672 - 677, Issue Special, July 2003

 Abstract        Full Text (168.1K)              

Gaston N'Guerekata - Department of Mathematics, Morgan State University, Baltimore, Maryland 21251, United States (email)

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.

Keywords:  Weak almost periodicity, optimal mild solutions, semigroups of linear operators, Banach spaces.
Mathematics Subject Classification:  Primary: 34C27, 35B15; Secondary: 34G10.

Received: July 2002;      Revised: April 2003;      Published: April 2003.