This paper investigated boundedness and global asymptotic stability of a certain second order nonlinear differential equation with damping using Lyapunov second method and eigenvalue approach. The critical point of the system was found to have multiple equilibria due to the cubic nature of the equation. Different regions of stability and instability were observed for different equilibria. The existence of total derivative confirmed boundedness of the solution. The damping effect was negligible. Mathcad software was used to illustrate the numerical behavior of the solutions. The results show that out of the three equilibrium points obtained, only two of them were asymptotically stable. Our results improve and extend some results in literature.

boundedness, stability, oscillator, damping, Lyapunov function.

Received: May 7, 2024; Accepted: August 13, 2024; Published: August 20, 2024

How to cite this article: E. O. Eze, U. E. Obasi, R. N. Ujumadu, M. O. Onuma, I. Udo and O. T. Oko, Boundedness and global asymptotic stability of a certain second order nonlinear differential equation with damping, Universal Journal of Mathematics and Mathematical Sciences 20(2) (2024), 73-92. http://dx.doi.org/10.17654/2277141724006

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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