STOCHASTIC EVOLUUTION EQUATIONS WITH MONOTONE NONLINEARITY IN Lp SPACES

Abstract

In this paper, we study semilinear stochastic evolution equations with semimonotone nonlinearity and multiplicative noise in L p spaces for 2 ≤ p < ∞. We do not impose any coercivity or Lipschitz condition on the nonlinear part of equations. We prove the existence, uniqueness and measurability of the mild solutions.The proofs of the existence and uniqueness are based on a version of the Itˆ o type inequality which is stronger than analogues inequalities.