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

International audienceIn 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