Càdlàg Skorokhod problem driven by a maximal monotone operator

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