A. A. Adeyanju, M. O. Omeike, J. O. Adeniran, and B. S. Badmus
Stability and Boundedness Theorems of Solutions of Certain Systems of Differential Equations
Dynamic Systems and Applications 34 (2025)  1-22

https://doi.org/10.46719/dsa2025.34.01

ABSTRACT.
In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to two systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some new results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations studied. Finally, we construct two numerical examples to show how valid our results are.

AMS (MOS) Subject Classification. 34K20.

Key Words and Phrases. Aizermann, boundedness, stability, first order, Lyapunov function.