SPDEs with two reflecting walls and two singular drifts

We study SPDEs with two reflecting walls Λ1<Λ2Λ1<Λ2 and two singular drifts c1(X−Λ1)ϑ, c2(Λ2−X)ϑ, driven by space–time white noise. First, we establish the existence and uniqueness of the solutions X   for ϑ≥0ϑ≥0, which satisfy Λ1≤X≤Λ2Λ1≤X≤Λ2. Second, we obtain the following pathwise properties of the solutions X  . If ϑ>3ϑ>3, then a.s. Λ1