Geodesic
Boundedness of Certain System of Second Order Differential Equations
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 5, p. 787 .

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This work is concerned with the ultimate boundedness of solutions of the system of vector differential equations \begin{equation*} \dot{X}=H(Y),\quad \dot{Y}=-F(X,Y)Y-G(X)+P(t,X,Y), \end{equation*} where $t\in\mathbb{R}^+,\ X=X(t)$, $Y=Y(t)\in \mathbb{R}^n$, $F:\mathbb{R}^n×\mathbb{R}^n\to\mathbb{R}^{n×n}, \ G,H:\mathbb{R}^n\to\mathbb{R}^n \ \mbox{and} \ P:\mathbb{R}^+×\mathbb{R}^n×\mathbb{R}^n\to\mathbb{R}^n.$ By using a Lyapunov function as a basic technique, we prove that the solutions of the system of equations are ultimately bounded. In addition, result obtained includes and improves some related results in literature.
Classification : 34C11
Keywords: boundedness, Lyapunov function, differential equations of second order 
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     author = {M. O. Omeike and A. A. Adeyanju and D. O. Adams and A. L. Olutimo},
     title = {Boundedness of {Certain} {System} of {Second} {Order} {Differential} {Equations}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {787 },
     publisher = {mathdoc},
     volume = {45},
     number = {5},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2021_45_5_a9/}
}
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M. O. Omeike; A. A. Adeyanju; D. O. Adams; A. L. Olutimo. Boundedness of Certain System of Second Order Differential Equations. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 5, p. 787 . http://geodesic.mathdoc.fr/item/KJM_2021_45_5_a9/