Abstract
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 dynamical systems method (DSM) for solving this 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 B( u) − f = 0 with monotone C loc 2 operators B.
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