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

TUNÇ C.

APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, cilt.12, sa.2, ss.813-842, 2017 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 2
  • Basım Tarihi: 2017
  • Dergi Adı: APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.813-842
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.