Geodesic
Asymptotic behavior of the solutions to a class of second-order differential systems
Electronic journal of differential equations, Tome 2001 (2001)
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 
@article{EJDE_2001__2001__a45,
     author = {Nenov,  Svetoslav Ivanov},
     title = {Asymptotic behavior of the solutions to a class of second-order differential systems},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0964.34038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a45/}
}
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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__a45/