Ramm, Alexander G.2011-06-152011-06-152010-02-01http://hdl.handle.net/2097/9249Sufficient conditions are given for an implicit function theorem to hold. The result is established by an application of the Dynamical Systems Method (DSM). It allows one to solve a class of nonlinear operator equations in the case when the Fr´echet derivative of the nonlinear operator is a smoothing operator, so that its inverse is an unbounded operator.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 Method (DSM)Hard implicit function theoremNewton’s methodArticle (author version)