An implicit function theorem for one-sided Lipschitz mappings

Wolf Jürgen Beyn, Janosch Rieger

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

Implicit function theorems are derived for nonlinear set valued equations that satisfy a relaxed one-sided Lipschitz condition. We discuss a local and a global version and study in detail the continuity properties of the implicit set-valued function. Applications are provided to the Crank-Nicolson scheme for differential inclusions and to the analysis of differential algebraic inclusions.

Original languageEnglish
Pages (from-to)343-359
Number of pages17
JournalSet-Valued and Variational Analysis
Volume19
Issue number3
DOIs
Publication statusPublished - Sep 2011
Externally publishedYes

Keywords

  • Differential (algebraic) inclusions
  • One-sided Lipschitz condition
  • Set valued implicit function theorem

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