Hard Implicit Function Theorem via the DSM
arXiv:0909.05019 citations
Originality Incremental advance
AI Analysis
Theoretical advancement for solving ill-posed nonlinear operator equations in functional analysis.
The paper provides sufficient conditions for a hard implicit function theorem using the Dynamical Systems Method (DSM), enabling solution of nonlinear operator equations where the Fréchet derivative is smoothing and its inverse is unbounded.
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 Fréchet derivative of the nonlinear operator is a smoothing operator, so that its inverse is an unbounded operator.