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An Implicit Function Theorem for One-sided Lipschitz Mappings |
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| Authors: | Wolf-Jürgen Beyn Janosch Rieger |
| Institution: | (1) Mathematical Reviews, American Mathematical Society, 416 Fourth Street, Ann Arbor, 48105, Church Street, MI, USA;(2) Department of Mathematics, University of Washington, PO Box 354350, Seattle, WA 98195-4350, USA |
| 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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