Pseudo almost automorphic solutions to non autonomous third order differential equation with multiple deviating arguments

Abstract

The pseudo almost automorphic solutions of non-autonomous third-order differential equation with multiple delays is investigated. By some sufficient conditions, we obtain the uniformly bounded of the solutions. Moreover, by Banach fixed point theorem we obtain the existence and uniqueness of the solutions. In addition, by suitable Laypunov functions, we give the globally exponential stability of the pseudo almost automorphic solutions. Finally, a numerical example is given to illustrate our results.