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