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arXiv.org e-Print Archive
Preprint . 2015
Data sources: arXiv.org e-Print Archive
https://dx.doi.org/10.48550/ar...
Article . 2015
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Global invertibility and implicit function theorems by mountain pass theorem

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2015Embargo end date: 01 Jan 2015Publisher:arXiv
Authors: Bors, Dorota; Stańczy, Robert;

doi: 10.48550/arxiv.1510.07871

arXiv: 1510.07871

Global invertibility and implicit function theorems by mountain pass theorem

Abstract

We formulate some global invertibility and implicit function theorems. We extend the result of Idczak, Skowron and Walczak on the invertibility of the operators to the case of the operators with critical points. The proof relies on the Mountain Pass Theorem combined with the Palais-Smale condition guaranteeing the claim by the invertibility of the first or the third derivative. I. e. how to solve $x^3=y$?

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Keywords

Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, FOS: Mathematics, Functional Analysis (math.FA), Analysis of PDEs (math.AP)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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