Stability of stochastic partial differential equations with infinite delays

摘要

In this paper, we study the existence and the asymptotical stability in p-th moment of mild solutions to stochastic partial differential equations with infinite delays {dx(t)=[Ax(t)+f(t,x(t−τ(t)))]dt+g(t,x(t−δ(t)))dW(t),t≥0,x0(⋅)=ξ∈DF0b([m(0),0],H) where t−τ(t),t−δ(t)→∞ with delays τ(t),δ(t)→∞ as t→∞. Our method for investigating the stability of solutions is based on the fixed point theorem.