Ekeland's inverse function theorem in graded Fréchet spaces revisited for multifunctions

In this paper, we present some inverse function theorems and implicit function theorems for set-valued mappings between Fréchet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of diffe...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 457; no. 2; pp. 1403 - 1421
Main Authors Huynh, Van Ngai, Théra, Michel
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.01.2018
Subjects
Contingent derivative
Ekeland's variational principle
Fréchet space
Implicit multifunction theorem
Inverse function theorem
Nash–Moser theorem
Fréchet space
Implicit multifunction theorem
Nash–Moser theorem
Contingent derivative
Ekeland's variational principle
Inverse function theorem
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Summary:In this paper, we present some inverse function theorems and implicit function theorems for set-valued mappings between Fréchet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Fréchet spaces with non-smooth data is given.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.07.040