Global invertibility and implicit function theorems by mountain pass theorem

2015/10/27 by Dorota Bors, Bors, Dorota, Robert Stańczy +1
Engineering · Mathematics · #Advanced Topics in Algebra #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods for differential equations #Stability and Controllability of Differential Equations #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.1510.07871

arxiv created 2015/10/27 · openalex publication_date 2015/10/27 · arxiv updated 2015/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 x³=y?

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