Document Type : Research Paper
Department of Mathematics Faculty of Arts and Sciences Gaziantep University 27310, Gaziantep, Turkey.
Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, VAN, Turkey.
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-Krasovskiˇı 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.