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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2022-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2022/1021461 |
| _version_ | 1798040898838200320 |
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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. |
| first_indexed | 2024-04-11T22:14:02Z |
| format | Article |
| id | doaj.art-d8b82ee26475413587bfe4db516cb2b9 |
| institution | Directory Open Access Journal |
| issn | 1687-0409 |
| language | English |
| last_indexed | 2024-04-11T22:14:02Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj.art-d8b82ee26475413587bfe4db516cb2b92022-12-22T04:00:29ZengHindawi LimitedAbstract 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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