On qualitative analyses of nonlinear delay differential equations of third order

Abstract

The authors of this paper examine uniformly asymptotically stability (UAS), uniformly boundedness (UB), ultimately uniformly boundedness  (UUB)  and existence of periodic solutions (EPSs) of certain nonlinear delay differential equations (DDEs) of third order with multiple constant delays. They prove two results and give a corollary on these properties of solutions. The main results of this paper have sufficient conditions and the technique of the proofs for these results is based on construction of a proper Lyapunov- Krasovski? function (LKF). This paper has novel results to the theory of DDEs of third order and fills the gaps related to  the mentioned concepts.