New qualitative results to delay integro-differential equations

Tunç O.

INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, cilt.13, sa.2, ss.1131-1141, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.22075/ijnaa.2022.25079.2912
  • Dergi Adı: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.1131-1141
  • Anahtar Kelimeler: DIDE, Lyapunov-Razumikhin method, stability, instability, boundedness, integrability, STABILITY PROPERTIES, ASYMPTOTIC STABILITY, BOUNDEDNESS, RAZUMIKHIN, SYSTEMS
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This work deals with various qualitative analyses of solutions of a certain delay integro-differential equation (DIDE). We prove here six new theorems including sufficient conditions, on uniformly stability (US), boundedness, asymptotically stability (AS), exponentially stability (ES), integrability and instability of solutions, respectively. By defining a suitable Lyapunov function (LF) and using the Razumikhin method (RM), the proofs of the theorems are provided. We gave two examples to demonstrate applications of the established new conditions.