Dynamical Systems Method for ill-posed equations with monotone operators
  Consider an operator equation (*) $B(u)-f=0$ in a real Hilbert space.   Let us call this equation ill-posed if the operator $B'(u)$ is not boundedly invertible, and well-posed otherwise. The DSM (dynamical systems method) for solving equation (*) consists of a construction of 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 minimal-norm solution to the equation $B(u)=f$.   A global convergence theorem is proved for DSM for equation (*) with monotone $C_{loc}^2$ operators $B$. 
A.G.Ramm