Ramm, Alexander G.Hoang, N. S.2011-06-152011-06-152011-06-15http://hdl.handle.net/2097/9250An evolution equation, arising in the study of the Dynamical Systems Method (DSM)for solving equations with monotone operators, is studied in this paper. The evolution equation is a continuous analog of the regularized Newton method for solving ill-posed problems with monotone nonlinear operators F. Local and global existence of the unique solution to this evolution equation are proved, apparently for the first time, under only the assumption that F′(u) exists and is continuous with respect to u. The earlier published results required more smoothness of F. The Dynamical Systems Method (DSM) for solving equations F(u)=0 with monotone Fr´echet differentiable operator F is justified under the above assumption apparently for the first time.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).http://rightsstatements.org/vocab/InC/1.0/Dynamical Systems Method (DSM)Nonlinear operator equationsMonotone operatorsArticle (publisher version)