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On C(n)- almost periodic solutions to some nonautonomous differential equations in Banach spaces

Baillon J-B., Blot J., N'Guérékata G.M., Pennequin D.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 2

263-273

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 c R, where A(t) generates an exponentially stable family of operators [...] -almost periodic function with values in a Banach space X. We also study a Volterra-like equation with a C(n)-almost periodic solution.