Geodesic
Stability and boundedness of solutions of nonlinear vector differential equations of third order
Archivum mathematicum, Tome 50 (2014) no. 2, pp. 101-106 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The paper studies the equation \begin{equation*}\dddot{X}+\Psi (\dot{X})\ddot{X}+\Phi (X)\dot{X}+cX=P(t) \end{equation*} in two cases: (i) $P(t)\equiv 0$, (ii) $P(t)\ne 0$. In case (i), the global asymptotic stability of the solution $X=0$ is studied; in case (ii), the boundedness of all solutions is proved.
The paper studies the equation \begin{equation*}\dddot{X}+\Psi (\dot{X})\ddot{X}+\Phi (X)\dot{X}+cX=P(t) \end{equation*} in two cases: (i) $P(t)\equiv 0$, (ii) $P(t)\ne 0$. In case (i), the global asymptotic stability of the solution $X=0$ is studied; in case (ii), the boundedness of all solutions is proved.
DOI : 10.5817/AM2014-2-101
Classification : 34C11, 34D05, 34D20, 34D40
Keywords: boundedness; stability; Liapunov function; differential equations of third order 
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Omeike, M. O. Stability and boundedness of solutions of nonlinear vector differential equations of third order. Archivum mathematicum, Tome 50 (2014) no. 2, pp. 101-106. doi: 10.5817/AM2014-2-101

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