Implicit function theorem via the DSM

Ramm, Alexander G.

doi:10.1016/j.na.2009.09.032

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Implicit function theorem via the DSM

Ramm, Alexander G.

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.

Keywords: Dynamical Systems Method (DSM); Hard implicit function theorem; Newton’s method

Journal: Nonlinear Analysis: Theory, Methods, and Applications, Volume: 72, Issue: 3-4, Starting Page: 1916, Ending Page: 1921

Date: 2010

Publisher URL: http://doi.org/10.1016/j.na.2009.09.032

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Record URL: http://hdl.handle.net/2097/9249

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