Existence and uniqueness theorems are given for RODEs under classical and Carathéodory
assumptions. In the latter case the measurability of solutions is also established. Conditions …

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial
differential equations with slow and fast time scales, or large and small spatial scales. The …

This paper is concerned with the asymptotic behaviour of solutions to a class of non-
autonomous stochastic nonlinear wave equations with dispersive and viscosity dissipative …

This book offers an introduction to the theory of non-autonomous and stochastic dynamical
systems, with a focus on the importance of the theory in the Applied Sciences. It starts by …

We investigate the incremental stability properties of Ito stochastic dynamical systems.
Specifically, we derive a stochastic version of nonlinear contraction theory that provides a …

We first prove the existence and uniqueness of pullback and random attractors for abstract
multi-valued non-autonomous and random dynamical systems. The standard assumption of …

Invariant manifolds are fundamental tools for describing and understanding nonlinear
dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite …

Page 1 MEMOIRS Of the American Mathematical Society Number 9, 17 The Stable Manifold
Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential …

In this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice
dynamical system with a multiplicative noise. We do not assume any Lipschitz condition on …

The main aim of this work is to provide some general and unified results on the existence,
regularity and finite fractal dimension estimates of pullback random attractors for a wide …