On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces

In this paper, we establish a generalization of the Galewski-Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence...

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Main Authors: Guy Degla, Cyrille Dansou, Fortuné Dohemeto
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2022/1021461
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author Guy Degla
Cyrille Dansou
Fortuné Dohemeto
author_facet Guy Degla
Cyrille Dansou
Fortuné Dohemeto
author_sort Guy Degla
collection DOAJ
description In this paper, we establish a generalization of the Galewski-Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence, uniqueness, and possible continuity of global implicit functions that parametrize the set of zeros of locally Lipschitz functions. Our methods rely on a nonsmooth critical point theory based on a generalization of the Ekeland variational principle.
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spelling doaj-art-d8b82ee26475413587bfe4db516cb2b92025-08-20T02:21:20ZengWileyAbstract and Applied Analysis1687-04092022-01-01202210.1155/2022/1021461On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean SpacesGuy Degla0Cyrille Dansou1Fortuné Dohemeto2Institut de Mathématiques et de Sciences PhysiqueInstitut de Mathématiques et de Sciences PhysiqueInstitut de Mathématiques et de Sciences PhysiqueIn this paper, we establish a generalization of the Galewski-Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence, uniqueness, and possible continuity of global implicit functions that parametrize the set of zeros of locally Lipschitz functions. Our methods rely on a nonsmooth critical point theory based on a generalization of the Ekeland variational principle.http://dx.doi.org/10.1155/2022/1021461
spellingShingle Guy Degla
Cyrille Dansou
Fortuné Dohemeto
On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces
Abstract and Applied Analysis
title On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces
title_full On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces
title_fullStr On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces
title_full_unstemmed On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces
title_short On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces
title_sort on nonsmooth global implicit function theorems for locally lipschitz functions from banach spaces to euclidean spaces
url http://dx.doi.org/10.1155/2022/1021461
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AT cyrilledansou onnonsmoothglobalimplicitfunctiontheoremsforlocallylipschitzfunctionsfrombanachspacestoeuclideanspaces
AT fortunedohemeto onnonsmoothglobalimplicitfunctiontheoremsforlocallylipschitzfunctionsfrombanachspacestoeuclideanspaces