Cà dlà g Skorokhod problem driven by a maximal monotone operator

The article deals with the existence and uniqueness of the solution of the following differential equation (a càdlàg Skorokhod problem) driven by a maximal monotone operator, and with singular input generated by the càdlàg function m:{dxt+A(xt)(dt)+dktd∋dmt,t≥0,x0=m0, where kd is a pure jump function. The jumps outside of the constrained domain D(A)¯ are counteracted through the generalized projection Π by taking xt=Π(xt−+Δmt), whenever xt−+Δmt∉D(A)¯. Approximations of the solution based on discretization and Yosida penalization are also considered.