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

Guy Degla, Cyrille Dansou and Fortuné Dohemeto

Abstract and Applied Analysis, 2022, vol. 2022, issue 1

Abstract: 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.

Date: 2022
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https://doi.org/10.1155/2022/1021461

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2022:y:2022:i:1:n:1021461

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