Almost automorphic solutions to some damped second-order differential equations

In this paper we make extensive use of dichotomy tools and the well-known Schauder fixed point principle to study and obtain the existence of almost automorphic solutions to some nonautonomous damped second-order differential equations. To illustrate our abstract result, we study the existence of almost automorphic solutions to the so-called plate-like equation.

► Techniques: use of exponential dichotomy. ► Use of Schauder fixed-point principle. ► Use of evolution families and interpolation spaces. ► Results: existence of almost automorphic solutions to nonautonomous differential equations. ► Existence of almost automorphic solutions to some damped second-order differential equations.