  An evolution equation, arising in the study of the Dynamical Systems Method
(DSM) for solving equations with monotone operators, is studied in this paper.
The evolution equation is a continuous analog of the regularized Newton method
for solving ill-posed problems with monotone nonlinear operators $F$. Local and
global existence of the unique solution to this evolution equation are proved,
apparently for the firs time, under the only assumption that $F'(u)$ exists and
is continuous with respect to $u$. The earlier published results required more
smoothness of $F$. The Dynamical Systems method (DSM) for solving equations
$F(u)=0$ with monotone Fr\'echet differentiable operator $F$ is justified under
the above assumption apparently for the first time.
