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

Abstract

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.

Keywords:

• Pseudo almost automorphic solution
• double measure
• mixed delays

2020 Mathematics Subject Classifications:

• 34A34
• 34C27
• 34C60
• 34D20
• 92B20

Disclosure statement

No potential conflict of interest was reported by the author(s).