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

Commun. Math. Anal.
Volume 8, Number 2 (2010), 103 - 124

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

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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.