Hoang, N. S.Ramm, Alexander G.2011-05-102011-05-102010-07-04http://hdl.handle.net/2097/9094This paper is a review of the authors’ results on the DSM (Dynamical Systems Method) for solving operator equation (*) F(u) = f. It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F. It is assumed that F is continuously Fr´echet differentiable, but no smoothness assumptions on F0(u) are imposed. The DSM for solving equation (*) is developed. Under weak assumptions global existence of the solution u(t) is proved, the existence of u(1) is established, and the relation F(u(1)) = f is obtained. The DSM is developed for a stable solution of equation (*) when noisy data f are given, kf − f k .This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).dynamical systems methodsnonlinear operator equationsmonotone operatorsdiscrepancy principlesmoothness assumptionsArticle (author version)