A remark on the qualitative conditions of nonlinear IDEs

Tunç C.

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, cilt.15, sa.3, ss.905-922, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 3
  • Basım Tarihi: 2020
  • Dergi Adı: INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.905-922
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, the stability (S), asymptotic stability (AS), uniform stability (US) of null solution and boundedness of solutions of non-linear Volterra integro-differential equations (IDEs) are investigated by means of the Lyapunov-Krasovskii method (LKM). Four new theorems are provided on the mentioned concepts for the considered (IDEs). Compared with past related results in the literature, our conditions are simple, weaker and convenient for testing and applications. The obtained results also improve and extend the past related results. Finally, two numerical examples are provided to illustrate the applications of our results.