On stability, boundedness, and square integrability of solutions of certain third order neutral differential equations. (English) Zbl 07584125

Graef, John R.; Beldjerd, Djamila; Remili, Moussadek

Math. Bohem. 147, No. 3, 285-299 (2022).

The authors of this paper consider two nonlinear neutral differential equations of third order with two constant delays. They constructed some new sufficient conditions under which the zero solution of the first neutral differential equation of third order is uniformly asymptotically stable and all solutions of the second neutral differential equation of third order are bounded and square integrable. Hence, three new theorems are proved on the concepts just mentioned, respectively. The technique of the proofs depends on Lyapunov-Krasovskii functional method. Here, a new Lyapunov-Krasovskii functional is defined and hence the proofs of the theorems are provided. The results of this paper are new and correct, and they also have new contributions to the theory of functional differential equations. Finally, in particular case, an example is given to provide the numerical applications of the given results and illustrations.

Reviewer: Cemil Tunç (Van)

MSC:

34K20	Stability theory of functional-differential equations
34K40	Neutral functional-differential equations

Keywords:

stability; boundedness; square integrability; Lyapunov-Krasovskii functional; neutral differential equation of third order