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

In this paper we prove the existence and uniqueness of $C^{(n)}$-almost periodic solutions to the nonautonomous ordinary differential equation $x^{\prime }(t)=A(t)x(t)+f(t)$, $t\in \mathbb{R}$, where $A(t)$ generates an exponentially stable family of operators $(U(t,s))$ $t\ge s$ 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.