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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Vydáno v:Axioms Ročník 14; číslo 3; s. 195
Hlavní autor: Cristea, Mihai
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 06.03.2025
Témata:
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
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms14030195