  If $F:H\to H$ is a map in a Hilbert space $H$, $F\in C^2_{loc}$, and there
exists $y$, such that $F(y)=0$, $F'(y)\not= 0$, then equation $F(u)=0$ can be
solved by a DSM (dynamical systems method). This method yields also a
convergent iterative method for finding $y$, and converges at the rate of a
geometric series. It is not assumed that $y$ is the only solution to $F(u)=0$.
Stable approximation to a solution of the equation $F(u)=f$ is constructed by a
DSM when $f$ is unknown but $f_\d$ is known, where $||f_\d-f||\leq \d$.
