Geodesic
Asymptotic behavior of the solutions to a class of second-order differential systems
Electronic Journal of Differential Equations, Tome 2001 (2001).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In the present paper it is proved that for any solution $x_1(t)$ of the system $M \ddot x + \dot x = f(t,x)$, for which $\lim\limits_{t\to\infty}\|\dot x_1(t)\|=0$, there exists a solution $x_2(t)$ of the system $\dot x = f(t,x)$ such that $\lim\limits_{t\to\infty}\|x_1(t)-x_2(t)\|=0$. Some generalizations of this result are also presented. The case $f(t,x)=-\nabla U(x)$ has been investigated explicitly.
Classification : 34D05, 34D10, 34E05
Keywords: asymptotic behaviour, gradient systems, T. wazewski's theorem 
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     author = {Nenov, Svetoslav Ivanov},
     title = {Asymptotic behavior of the solutions to a class of second-order differential systems},
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     volume = {2001},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a123/}
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Nenov, Svetoslav Ivanov. Asymptotic behavior of the solutions to a class of second-order differential systems. Electronic Journal of Differential Equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a123/