Skorohod problem and multivalued stochastic evolution equations in Banach spaces

Abstract

By solving a deterministic Skorohod problem in the framework of evolutional triple, we prove the existence and uniqueness of solutions to multivalued stochastic evolution equations involving maximal monotone operators. The existence and uniqueness of invariant measures associated with the solutions as Markov processes are also considered in the present paper. Moreover, we apply the results to stochastic differential equations with normal reflecting boundary conditions and with singular drift terms, as well as a class of multivalued nonlinear stochastic partial differential equations with possibly discontinuous coefficients.