On Inverse and Implicit Function Theorem for Sobolev Mappings

We extend Clarke’s local inversion theorem for Sobolev mappings. We use this result to find a general implicit function theorem for continuous locally Lipschitz mapping in the first variable and satisfying just a topological condition in the second variable. An application to control systems is give...

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Bibliographic Details
Published in:Axioms Vol. 14; no. 3; p. 195
Main Author: Cristea, Mihai
Format: Journal Article
Language:English
Published: Basel MDPI AG 06.03.2025
Subjects:
Analysis
Banach spaces
Control systems
Differential equations
implicit function theorem
local and global univalence
Numerical analysis
Ordinary differential equations
Sobolev mappings
Theorems
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:We extend Clarke’s local inversion theorem for Sobolev mappings. We use this result to find a general implicit function theorem for continuous locally Lipschitz mapping in the first variable and satisfying just a topological condition in the second variable. An application to control systems is given.
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content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms14030195