Hard Implicit Function Theorem via the DSM
Functional Analysis
2009-09-23 v2 Numerical Analysis
Abstract
Sufficient conditions are given for a hard 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.
Cite
@article{arxiv.0909.0501,
title = {Hard Implicit Function Theorem via the DSM},
author = {A. G. Ramm},
journal= {arXiv preprint arXiv:0909.0501},
year = {2009}
}