Lyapunov stability of differential inclusions with Lipschitz Cusco perturbations of maximal monotone operators

We give criteria for weak and strong invariant closed sets for differential inclusions given in $\mathbb{R}^{n}$ and governed by Lipschitz Cusco perturbations of maximal monotone operators. Correspondingly, we provide different characterizations for the\ associated strong Lyapunov functions. The resulting conditions only depend on the data of the system.