Abstract
The Lyapunov second method is an eigenvalue-based technique which consist of finding a Lyapunov function candidate for studying the stability of dynamical systems which is hard to deal with especially in most of nonlinear cases. Studying the stability and some of other qualitative behaviors based on the Lyapunov second method is research topic of actuality because of the wide range of applications of the differential equations. Many authors in the literature have used the second method of Lyapunov in the study of some qualitative behaviors from which the stability, the boundedness and the square integrability of solutions for various kinds of differential equations that are different in terms of the order, the linearity, the autonomy, the delay or the neutral case. The present paper contains two main results. The first part is dedicated to establish sufficient conditions that guarantee the boundedness and the square integrability of solutions for a given third order neutral differential equation with delay. The second part of this work is devoted to the purpose of breaking the barrier of reaching exponential stability for some cases of the previous third order differential equation using the direct method of Lyapunov. In the end of the paper, a concrete example is given to illustrate the obtained results.
Recommended Citation
Abdellaoui, Fatima and Rahmane, Mebrouk
(2024).
(R2099) Boundedness and Square Integrability in Neutral Differential Equations with Delay and Exponential Stability in Nonlinear Differential Equations of Third-order,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 20,
Iss.
1, Article 12.
Available at:
https://digitalcommons.pvamu.edu/aam/vol20/iss1/12