Cadlag Skorokhod problem driven by a maximal monotone operator

The article deals with existence and uniqueness of the solution of the following differential equation (a c`adl`ag Skorokhod problem) driven by a maximal monotone operator and with singular input generated by the c`{a}dl`{a}g function $m$: \left\{ \begin{array} [c]{l} dx_{t}+A\left( x_{t}\right) \left( dt\right) +dk_{t}^{d}\ni dm_{t} \,,~t\geq0,\\ x_{0}=m_{0}, \end{array} \right. where $k^d$ is a pure jump function. The jumps outside of the constrained domain $\overline{\mathrm{D}(A)}$ are counteracted through the generalized projection $\mathrm{\Pi }$, by taking $x_t=\mathrm{\Pi }(x_{t-}+\mathrm{\Delta }{m}_t)$, whenever $x_{t-}+\mathrm{\Delta }{m}_t\mathrm{\notin }\overline{\mathrm{D}(A)}$. Approximations of the solution based on discretization and Yosida penalization are considered.