Integration by parts on \(\delta\)-Bessel bridges, \(\delta>3\), and related SPDEs (Q1872333)

The author uses an integration by parts formula to study a white-noise driven semilinear partial differential equation on the spatial interval \([0,1]\) with Dirichlet boundary condition and with a singular drift of the form \(cu^3\), \(c> 0\). He proves existence and uniqueness of a nonnegative continuous adapted solution for every nonnegative coontinuous initial datum satisfying \(x(0)= x(1)= 0\). The ergodicity of the solution is also studied.