Asia Mathematika, Vol 9, issue 3, pages: 1--11.

New Results on Behavior of Solutions of Certain System of Third-Order Non-linear Differential Equations

Adetunji Adedotun Adeyanju
Department of Mathematics, Federal University of Agriculture Abeokuta, Nigeria.

Received: 08 Sep 2025 | Accepted: 02 Dec 2025 | Final Version: 31 Dec 2025

Abstract

In this article, provisions are made for sufficient conditions that guaranteed uniform asymptotic stability of the trivial solution and uniform boundedness of all solutions to a class of third-order non-linear differential equations. The direct method of Lyapunov is used to establish our results. Numerical examples are given together with the graphical representation of their solutions by Maple software as a justification for our findings.

Keywords:
Third order, Stability, Boundedness, Lyapunov function.

1. Introduction

The main intention of this article is to employ the Lyapunov direct method to address the problem of stability and boundedness behavior of solutions to the following equation \begin{equation}\label{1.5} X^{\prime \prime \prime} + r(t)\Psi(X, X^{\prime}) X^{\prime \prime} + q(t)\Phi(X, X^{\prime} ) X^{\prime} + \eta H(X) = P(t, X, X^{\prime}, X^{\prime \prime}), \end{equation}

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