Application of Methods of Ordinary Differential Equations to Global Inverse Function Theorems

We obtain a global inverse function theorem guaranteeing that if a smooth mapping of finite-dimensional spaces is uniformly nonsingular, then it has a smooth right inverse. Global implicit function theorems are obtained guaranteeing the existence and continuity of a global implicit function under th...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Differential equations Ročník 55; číslo 4; s. 437 - 448
Hlavní autoři: Arutyunov, A. V., Zhukovskiy, S. E.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.04.2019
Springer
Springer Nature B.V
Témata:
Difference and Functional Equations
Differential equations
Existence theorems
Hilbert space
Mapping
Mathematical optimization
Mathematics
Mathematics and Statistics
Methods
Ordinary Differential Equations
Partial Differential Equations
Smoothness
ISSN:0012-2661, 1608-3083
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:We obtain a global inverse function theorem guaranteeing that if a smooth mapping of finite-dimensional spaces is uniformly nonsingular, then it has a smooth right inverse. Global implicit function theorems are obtained guaranteeing the existence and continuity of a global implicit function under the condition that the mappings in question are uniformly nonsingular. The local Lipschitz property and the smoothness of the global implicit function are studied. The results are generalized to the case of mappings of Hilbert spaces.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266119040013