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An Implicit Function Theorem for One-sided Lipschitz Mappings

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.

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Author information

Correspondence to Wolf-Jürgen Beyn.

Additional information

Supported by CRC 701 ‘Spectral Structures and Topological Methods in Mathematics’, Bielefeld University.

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Beyn, W., Rieger, J. An Implicit Function Theorem for One-sided Lipschitz Mappings. Set-Valued Anal 19, 343–359 (2011). https://doi.org/10.1007/s11228-010-0162-8

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Keywords

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

Mathematics Subject Classifications (2010)

  • 47H10
  • 47N20
  • 34A60