https://gphjournal.org/index.php/m/issue/feed 2025-08-24T11:49:25+00:00 Dr. EKEKE, JOHN NDUBUEZE drekekejohn@gmail.com Open Journal Systems <p style="font-family: 'Segoe UI', sans-serif; font-size: 16px; color: #333;"><strong>GPH-International Journal of Mathematics (e-ISSN&nbsp;<a href="https://portal.issn.org/resource/ISSN/3050-9629" target="_blank" rel="noopener">3050-9645</a>)</strong> is a peer-reviewed, open-access journal dedicated to advancing research in mathematics. The journal publishes original research articles, comprehensive reviews, and survey papers covering both pure and applied mathematics, including topics such as algebra, analysis, geometry, number theory, and mathematical modeling. It provides a global platform for mathematicians and researchers to share innovative ideas, foster interdisciplinary collaboration, and contribute to the advancement of mathematical knowledge.</p> https://gphjournal.org/index.php/m/article/view/2055 2025-08-24T11:49:25+00:00 Ezugorie Ikechukwu Godwin ikegodezugorie@esut.edu.ng

<p>This paper investigated boundedness and global asymptotic stability of solutions of a class of certain second order nonlinear differential equation with damping using the Lyapunov second order and eigenvalue approach. Through the exploits of Schwartz inequality and assumptions on the inhomogeneous part, solutions of the Duffing equation were bounded and the equilibrium point was global asymptotically stable. Response to damping revealed that the damping effect was not negligible thereby reducing oscillations. Application of our results can be seen in the construction of door net where the trajectory returns to equilibrium as fast as possible. Furthermore, Mathcad software was used to analyze the behavior of the system which extends some results in literature. &nbsp;&nbsp;</p>

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