An Implicit Function Theorem for One-sided Lipschitz Mappings - Beyn, Wolf-Jürgen; Rieger, Janosch (Set-valued and variational analysis, 2011)
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.