Hard Implicit Function Theorem via the DSM

2009/09/02 by Ramm, A. G.
#47 47J05 #47J25 #47J25J05 #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.0909.0501

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 Fréchet derivative of the nonlinear operator is a smoothing operator, so that its inverse is an unbounded operator.

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