Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 12, pp. 1-9.
Title: Asymptotic behavior of the solutions of a class of second order
differential systems
Author: Svetoslav Ivanov Nenov (Univ. of Chemical Tech. and Metallurgy, Sofia, Bulgaria)
Abstract:
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.
Submitted April 4, 2000; December 28, 2000. Published January 30, 2001.
Math Subject Classifications: 34D05, 34D10, 34E05.
Key Words: asymptotic behaviour; gradient systems; T. Wazewski's theorem.