Geodesic
On \(C^{(n)}\)-Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces
Commentationes Mathematicae, Tome 46 (2006) no. 2, pp. 263-273 Cet article a éte moissonné depuis la source Annales Societatis Mathematicae Polonae Series

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In this paper we prove the existence and uniqueness of \(C^{(n)}\)-almost periodic solutions to the nonautonomous ordinary differential equation \(x'(t) = A(t)x(t) + f(t)\), \(t\in\mathbb{R}\), where \(A(t)\) generates an exponentially stable family of operators \((U (t, s))\) \(t\geq s\) and \(f\) is a \(C^{(n)}\)-almost periodic function with values in a Banach space \(X\). We also study a Volterra-like equation with a \(C^{(n)}\)-almost periodic solution.
DOI : 10.14708/cm.v46i2.5222
Mots-clés : \(C^{(n)}\)-almost periodic function, family of bounded operators, exponentially stable, Acquistapace-Terreni conditions, uniform spectrum of bounded functions 
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Jean-Bernard Baillon; Joël Blot; Gaston M. N'Guérékata; Denis Pennequin. On \(C^{(n)}\)-Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces. Commentationes Mathematicae, Tome 46 (2006) no. 2, pp.  263-273. doi: 10.14708/cm.v46i2.5222

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