An analysis for a special class of solution of a Duffing system with variable delays


Yazgan R.

AIMS MATHEMATICS, vol.6, no.10, pp.11187-11199, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 10
  • Publication Date: 2021
  • Doi Number: 10.3934/math.2021649
  • Title of Journal : AIMS MATHEMATICS
  • Page Numbers: pp.11187-11199
  • Keywords: Lyapunov function, Pseudo almost automorphic, Banach fixed point theorem, exponential stability, Duffing equation system, ALMOST-PERIODIC SOLUTIONS, NUMERICAL-SOLUTION, PSEUDO, EQUATIONS

Abstract

In this study, we are concerned the existence of pseudo almost automorphic (PAA) solutions and globally exponential stability of a Duffing equation system with variable delays. Some differential inequalities and the well-known Banach fixed point theorem are used for the existence and uniqueness of PAA solutions. Also, with the help of Lyapunov functions, sufficient conditions are obtained for globally exponential stability of PAA solutions. Since the PAA is more general than the almost and pseudo almost periodicity, this work is new and complementary compared to previous studies. In addition, an example is given to show the correctness of our results.