Implicit function theorem via the DSM
Date
2010-02-01
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Abstract
Sufficient 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.
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Keywords
Dynamical Systems Method (DSM), Hard implicit function theorem, Newton’s method