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

Guy Degla, Cyrille Dansou, Fortuné Dohemeto and Simeon Reich

Abstract and Applied Analysis, 2022, vol. 2022, 1-19

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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:1021461

DOI: 10.1155/2022/1021461

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