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

被引：5

作者：

Van Ngai, Huynh ^{[1
]}

Thera, Michel ^{[2
,3
]}

机构：

[1] Univ Quynhon, Dept Math, Quynhon, Vietnam

[2] Univ Limoges, Lab XLIM, UMR CNRS 6172, Limoges, France

[3] Federat Univ Australia, Ctr Informat & Appl Optimizat, Ballarat, Vic, Australia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 457卷 / 02期

基金：

澳大利亚研究理事会;

关键词：

Inverse function theorem; Frechet space; Nash-Moser theorem; Contingent derivative; Ekeland's variational principle; Implicit multifunction theorem; DIFFERENTIAL-EQUATIONS; IMPLICIT; NASH; MOSER;

D O I：

10.1016/j.jmaa.2017.07.040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present some inverse function theorems and implicit function theorems for set-valued mappings between Frechet 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 Frechet spaces with non-smooth data is given. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：1403 / 1421

页数：19

共 22 条

[1] [Anonymous], 1972, Ann. Sci. Ecole Norm. Sup.
[2] [Anonymous], 1991, OPERATEURS PSEUDO DI
[3] AUBIN J. P., 1990, Set-valued analysis, V2, DOI [10.1007/978-0-8176-4848-0, DOI 10.1007/978-0-8176-4848-0]
[4] On implicit multifunction theorems
Aze, D.
Benahmed, S.
[J]. SET-VALUED ANALYSIS, 2008, 16 (2-3): : 129 - 155
[5] Dontchev AL, 2014, Implicit Functions and Solution Mappings: A View from Variational Analysis, V2nd
[6] Openness stability and implicit multifunction theorems: Applications to variational systems
Durea, M.
Strugariu, R.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (03) : 1246 - 1259
[7] VARIATIONAL PRINCIPLE
EKELAND, I
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1974, 47 (02) : 324 - 353
[8] Ekeland I., 2014, PREPRINT
[9] An inverse function theorem in Frechet spaces
Ekeland, Ivar
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2011, 28 (01): : 91 - 105
[10] THE INVERSE FUNCTION THEOREM OF NASH AND MOSER
HAMILTON, RS
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 7 (01) : 65 - 222

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