Geodesic
Ultimate Boundedness of Solutions of Some System of Third-Order Nonlinear Differential Equations
Kragujevac Journal of Mathematics, Tome 49 (2025) no. 5, p. 727

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This paper presents sufficient conditions for the ultimate boundedness of solutions of some system of third-order nonlinear differential equations \begin{equation*}tackrel{...}{X}+\Psi(\dot{X})ḍot{X}+\Phi(X)\dot{X}+H(X)=P(t,X,\dot{X},ḍot{X}),\end{equation*} where $\Psi,\Phi$ are positive definite symmetric matrices, $H, P$ are $n-$vectors continuous in their respective arguments, $X\in\mathbb{R}^n$ and $t\in\mathbb{R}^+=[0,+\infty).$ We do not necessarily require $H(X)$ differentiable to obtain our results. By using the Lyapunov's direct (second) method and constructing a complete Lyapunov function, earlier results are generalized.
Classification : 34C11, 34D20
Keywords: ultimate boundedness, Lyapunov function, system of third-order nonlinear differential equations. 
Ayinla A. Abdurasid; Kehinde D. Aduloju; Musiliu T. Raji; Olufunke R. Vincent; Mathew O. Omeike. Ultimate Boundedness of Solutions of Some System of Third-Order Nonlinear Differential Equations. Kragujevac Journal of Mathematics, Tome 49 (2025) no. 5, p. 727 . http://geodesic.mathdoc.fr/item/KJM_2025_49_5_a5/
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     title = {Ultimate {Boundedness} of {Solutions} of {Some} {System} of {Third-Order} {Nonlinear} {Differential} {Equations}},
     journal = {Kragujevac Journal of Mathematics},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2025_49_5_a5/}
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