2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214356Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable and pseudo-unstable manifolds for a class of \emph{random} partial differential equations and \emph{stochastic} partial differential equations is shown. Unlike the invariant manifold theory for stochastic \emph{ordinary} differential equations, random norms are not used. The result is then applied to a nonlinear stochastic partial differential equation with linear multiplicative noise.Adv. Nonlinear Studies, in press, 2009Dynamical SystemsAnalysis of PDEsProbability37L55, 35R60; 58B99, 35L20text