Second‐order Neutral Stochastic Evolution Equations with Infinite Delay under Carathéodory Conditions

In this paper, we study a class of second‐order neutral stochastic evolution equations with infinite delay, in which the initial value belongs to the abstract space ℬ. We establish the existence and uniqueness of mild solutions for SNSEEIs under global and local Carathéodory conditions by means of the successive approximation. An application to the stochastic nonlinear wave equations with infinite delay is given to illustrate the theory.