  Consider an operator equation $F(u)=0$ in a real Hilbert space.
  Let us call this equation ill-posed if the operator
  $F'(u)$ is not boundedly invertible, and well-posed otherwise.
  If $F$ is monotone $C^2_{loc}(H)$ operator, then we construct a Cauchy
problem, which has the following properties:
  1) it has a global solution for an arbitrary initial data,
  2) this solution tends to a limit as time tends to infinity,
  3) the limit is the minimum norm solution to the equation $F(u)=0$.
  Example of applications to linear ill-posed operator equation is given.
