English

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.

Keywords

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}
}
R2 v1 2026-06-21T13:41:55.858Z