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

Author

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  • Guy Degla
  • Cyrille Dansou
  • Fortuné Dohemeto
  • Simeon Reich

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.

Suggested Citation

  • Guy Degla & Cyrille Dansou & Fortuné Dohemeto & Simeon Reich, 2022. "On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces," Abstract and Applied Analysis, Hindawi, vol. 2022, pages 1-19, July.
    • Handle: RePEc:hin:jnlaaa:1021461
    DOI: 10.1155/2022/1021461
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