On the qualitative behaviors of a functional differential equation of second order


TUNÇ C.

APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, vol.12, no.2, pp.813-842, 2017 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 2
  • Publication Date: 2017
  • Title of Journal : APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL
  • Page Numbers: pp.813-842

Abstract

The aim of this paper is first to investigate the stability of the zero solution to a new Lienard type equation with multiple variable delays by two different methods. The methods to be used in the proofs involve the Lyapunov-Krasovskii functional approach and the fixed point technique under an exponentially weighted metric, respectively. We make a comparison between the applications of these methods with the established conditions on the same stability problems. Then, we obtain three new results for uniformly stability and boundedness/uniformly boundedness of the solutions to the considered equation by the Lyapunov-Krasovskii functional approach. An example is given to verify the results obtained by the Lyapunov-Krasovskii functional approach. Our results complement and improve some recent ones in the literature.