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On C ( n ) -Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces

Jean-Bernard BaillonJoël BlotGaston M. N'GuérékataDenis Pennequin — 2006

Commentationes Mathematicae

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 , where A ( t ) generates an exponentially stable family of operators ( U ( t , s ) ) t 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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