On the stability, boundedness and asymptotic behaviour of solutions of differential equations of third-order

  • A. A. Adeyanju Department of Mathematics, Federal University of Agriculture Abeokuta, Nigeria.
  • S. A. Oni Department of Mathematics, Federal University of Agriculture Abeokuta, Nigeria.
  • D. O. Adams Department of Mathematics, Federal University of Agriculture Abeokuta, Nigeria.
  • S. A. Oni Department of Mathematics, Lagos state University Ojo, Nigeria.
  • A. L. Olutimo Department of Mathematics, Lagos state University Ojo, Nigeria.
DOI: https://doi.org/10.6084/zenodo.10384294
Keywords: Third order, stability, boundedness, asymptotic behaviour, non-linear, Lyapunov function

Abstract

In this paper, we construct a complete Lyapunov function which serves as a tool in providing sufficient conditions that ensure uniform asymptotic stability of the zero solution when p(t, x, y, z) ≡ 0; uniform ultimate boundedness and asymptotic behaviour of all solutions when p(t, x, y, z) ̸= 0 of a certain third order non-linear ordinary differential equation. The results in this paper are new and in some ways generalize and improve on some existing results in literature. Finally, we provide an example to justify the correctness of the theorems.

Published
2023-12-18
How to Cite
Adeyanju, A. A., Oni, S. A., Adams, D. O., Oni, S. A., & Olutimo, A. L. (2023). On the stability, boundedness and asymptotic behaviour of solutions of differential equations of third-order. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 9(2), 121 - 132. https://doi.org/10.6084/zenodo.10384294
Issue
Vol 9 No 2 (2023)
Section
Articles

Copyright (c) 2023 A. A. Adeyanju, S. A. Oni, D. O. Adams, S. A. Oni, A. L. Olutimo

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