2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109005We present a generalization of Krylov-Rozovskii's result on the existence and uniqueness of solutions to monotone stochastic differential equations. As an application, the stochastic generalized porous media and fast diffusion equations are studied for $σ$-finite reference measures, where the drift term is given by a negative definite operator acting on a time-dependent function, which belongs to a large class of functions comparable with the so-called $N$-functions in the theory of Orlicz spaces.36 pages, BiBoS-Preprint No. 06-02-205Probability76S05; 60H15text