<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, some qualitative behaviors of solutions for certain second-order nonlinear differential equation with damping and resonance effects are considered. By employing Lyapunov’s direct method, a complete Lyapunov function was used to investigate the stability of the system. Krasnoselskii’s fixed point theorem was used to establish sufficient conditions that guaranteed the existence and boundedness of a unique solution. The results show that the equilibrium point was asymptotically stable. Furthermore, a test for periodicity was conducted using the Bendixson criterion, and the results showed that the solution of the second-order nonlinear differential equation is aperiodic, which extends some results from the literature.</p>
</abstract>

In this paper, some qualitative behaviors of solutions for certain second-order nonlinear differential equation with damping and resonance effects are considered. By employing Lyapunov’s direct method, a complete Lyapunov function was used to investigate the stability of the system. Krasnoselskii’s fixed point theorem was used to establish sufficient conditions that guaranteed the existence and boundedness of a unique solution. The results show that the equilibrium point was asymptotically stable. Furthermore, a test for periodicity was conducted using the Bendixson criterion, and the results showed that the solution of the second-order nonlinear differential equation is aperiodic, which extends some results from the literature.

Existence, uniqueness, boundedness and stability of periodic solutions of a certain second-order nonlinear differential equation with damping and resonance effects

Enugu State University Science and Technology

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, some qualitative behaviors of solutions for certain second-order nonlinear differential equation with damping and resonance effects are...

Existence, uniqueness, boundedness and stability of periodic solutions of a certain second-order nonlinear differential equation with damping and resonance effects

Published Online: Dec 29, 2023

Page range: 109 - 124

DOI: https://doi.org/10.2478/bile-2023-0008

Keywords
Lyapunov function, Stability, Krasnoselskii’s fixed point theorem, Periodic solutions, Duffing’s equation

© 2023 Everestus Obinwanne Eze et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Existence, uniqueness, boundedness and stability of periodic solutions of a certain second-order nonlinear differential equation with damping and resonance effects

Published Online: Dec 29, 2023

Page range: 109 - 124

DOI: https://doi.org/10.2478/bile-2023-0008

KeywordsLyapunov function, Stability, Krasnoselskii’s fixed point theorem, Periodic solutions, Duffing’s equation

© 2023 Everestus Obinwanne Eze et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Lyapunov function, Stability, Krasnoselskii’s fixed point theorem, Periodic solutions, Duffing’s equation