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On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

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  • Jing Cui
  • Litan Yan

Abstract

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square‐mean almost automorphic functions under non‐Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square‐mean almost automorphic mild solutions. Some known results are generalized and improved.

Suggested Citation

  • Jing Cui & Litan Yan, 2012. "On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:870831
    DOI: 10.1155/2012/870831
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    References listed on IDEAS

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    1. Bezandry, Paul H., 2008. "Existence of almost periodic solutions to some functional integro-differential stochastic evolution equations," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2844-2849, December.
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