Electron. J. Diff. Eqns., Vol. 2001(2001), No. 12, pp. 1-9.

Asymptotic behavior of the solutions of a class of second order differential systems

Svetoslav Ivanov Nenov

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.

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Svetoslav Ivanov Nenov
Department of Mathematics
University of Chemical Technology and Metallurgy
8, Kliment Ohridsky blvd., Sofia 1756, Bulgaria
e-mail: s.nenov@uctm.edu, s_nenov@hotmail.com

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