On $C^{(n)}$- Almost Periodic Solutions to some nonautonomous Differential Equations in Banach Spaces - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annales Societatis Mathematicae Polonae, Serie I Année : 2006

On $C^{(n)}$- Almost Periodic Solutions to some nonautonomous Differential Equations in Banach Spaces

Résumé

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.
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Dates et versions

hal-00617458 , version 1 (29-08-2011)

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  • HAL Id : hal-00617458 , version 1

Citer

Jean-Bernard Baillon, Joël Blot, Gaston Mandata N'Guérékata, Denis Pennequin. On $C^{(n)}$- Almost Periodic Solutions to some nonautonomous Differential Equations in Banach Spaces. Annales Societatis Mathematicae Polonae, Serie I, 2006, XLVI (2), pp.263-273. ⟨hal-00617458⟩

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