Second-order nonlinear differential equations: existence, uniqueness and global exponential stability of doubly measure pseudo-almost automorphic solutions

The main aim of this work is to study a second-order nonlinear differential equation with mixed delay and time-varying coefficients. By employing the fixed-point theorem and some properties of the doubly measure pseudo almost automorphic functions, we prove the existence, uniqueness and global exponential stability of doubly measure pseudo-almost automorphic solution to the second-order delay differential equation. Our approach generalizes the classical results on weighted pseudo almost automorphic functions. Finally, a numerical example is provided to illustrate the effectiveness and feasibility of the obtained results.