Asymptotic behavior for neutral stochastic partial differential equations with infinite delays

Asymptotic behavior for neutral stochastic partial differential equations with infinite delays∗

This paper is concerned with the existence and asymptotic behavior of mild solutions to a class of non-linear neutral stochastic partial differential equations with infinite delays. By applying fixed point principle, we present sufficient conditions to ensure that the mild solutions are exponentially stable in pth-moment (p ≥ 2) and almost surely exponentially stable. An example is provided to ...

The Asymptotic Behavior for Second-Order Neutral Stochastic Partial Differential Equations with Infinite Delay

Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays

and Applied Analysis 3 (iii) X 0 (⋅) = φ ∈ BF([m(0), 0],H), where

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Asymptotic stability of impulsive stochastic partial differential equations with infinite delays

Article history: Received 29 January 2009 Available online 6 February 2009 Submitted by Goong Chen