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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 Cauchyproblem, 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

Global convergence for ill-posed equations with monotone operators: the dynamical systems method