On the existence of periodic solutions of third order delay differential equations

Erdur S., Tunç C.

Computational Methods for Differential Equations, vol.11, no.2, pp.319-331, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.22034/cmde.2022.50862.2112
  • Journal Name: Computational Methods for Differential Equations
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.319-331
  • Keywords: Delay, Differential equation, Existence, LKF, Periodic solutions, Third order
  • Van Yüzüncü Yıl University Affiliated: Yes


This work deals with the existence of periodic solutions (EPSs) to a third order nonlinear delay differential equation (DDE) with multiple constant delays. For the considered DDE, a theorem is proved, which includes sufficient criteria related to the EPSs. The technique of the proof depends on Lyapunov-Krasovskiı̌ functional (LKF) approach. The obtained result extends and improves some results that can be found in the literature. In a particular case of the considered DDE, an example is provided to show the applicability of the main result of this paper.