Forrás: | Ladde, G. S. (ed.) et al., Dynamic systems and applications. Volume 3. Proceedings of the 3rd international conference, Morehouse College, Atlanta, GA, USA, May 26-29, 1999. Atlanta, GA: Dynamic Publishers. 297-304 (2001). [ISBN 0-96-403983-4/hbk] |

Absztrakt: | The paper has been written by a prominent scientist in the area
of functional-differential equations. A nonautonomous system
of functional-differential equations with delay $$ \frac{dx(t)}{dt}=F(t,x_t),\quad
F(t,0)\equiv 0,\tag 1$$ is considered, and the asymptotic stability
of its solution $$ x(t)\equiv 0\tag 2$$ is studied. Sufficient
conditions for asymptotic stability and uniform asymptotic stability
of solution (2) to equation (1) with finite delays are formulated
by the method of Lyapunov functionals. The derivatives of the
functionals with respect to the equations are negative semidefinite
in terms of either $|x(t)|$ or $L_2$-norm of segment $x_t$ and
may depend explicitly on time $t$. The theorems do not require
the boundedness of the right-hand sides in the equations.}
\RV{Alexander Olegovich Ignatyev (Donetsk) |