Fixed Points and Stability of Stochastic Neutral Partial Differential Equations with Infinite Delays

Abstract

Abstract In this article, we study the existence and the asymptotical stability in mean square of mild solutions to stochastic neutral partial differential equations with infinite delays where t − τ(t), t − δ(t), t − ρ(t) → ∞ with delays τ(t), δ(t), ρ(t) → ∞ as t → ∞. Our method for investigating the stability of solutions is based on the fixed point theorem.