Absztrakt: | The paper has been written by a famous 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 asymptotic stability
and uniform asymptotic stability of its solution $$ x(t)\equiv
0\eqno(2) $$ are studied. It is assumed that the right-hand sides
of equation (1) are unbounded functions in $t$. Sufficient conditions
for the 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 are applied to
linear and nonlinear retarded functional-differential equations
with one delay and with distributed delays.}
\RV{Alexander Olegovich Ignatyev (Donetsk) |