Almost periodic solutions for some higher-order nonautonomous differential equations with operator coefficients

Keywords: Schauder fixed point principle Exponentially stable Acquistapace–Terreni conditions Evolution families Almost periodic Higher-order differential equation with operator coefficients Wave equation with fractional damping a b s t r a c t In this paper, we make extensive use of the well-known Schauder fixed point principle and the exponential stability of the evolution family involved to study and obtain the existence of almost periodic mild solutions to some classes of nonautonomous higher-order differential equations with operator coefficients in a separable infinite dimensional complex Hilbert space. To illustrate our main result, we study and obtain the existence of an almost periodic mild solution to a wave equation with fractional damping.