Existence of Square-Mean Almost Periodic Solutions to Some Stochastic Hyperbolic Differential Equations with Infinite Delay

Abstract

In this paper, we make extensive use of the well-known Krasnoselskii fixed point theorem to obtain the existence of square-mean almost periodic solutions to some classes of hyperbolic stochastic evolution equations with infinite delay. Next, the existence of square-mean almost periodic solutions to not only the heat equation but also to a boundary value problem with infinite delay arising in control systems are studied.