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Almost automorphic solutions of semilinear evolution equations

Authors:	Jerome A Goldstein Gaston M N'Gué ré kata

Institution:	Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152-3240 ; Department of Mathematics, Morgan State University, Baltimore, Maryland 21251

Abstract:	We are concerned with the semilinear differential equation in a Banach space $\mathbb{X}$ , $\begin{displaymath}x'(t)=Ax(t)+F(t,x(t)), t\in \mathbb{R}\, ,\end{displaymath}$ where generates an exponentially stable -semigroup and $F(t,x): \mathbb{R}\times \mathbb{X}\to \mathbb{X}$ is a function of the form . Under appropriate conditions on and , and using the Schauder fixed point theorem, we prove the existence of an almost automorphic mild solution to the above equation.

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