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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, Hindawi, vol. 2012, pages 1-25, July.
    • Handle: RePEc:hin:jnlaaa:870831
    DOI: 10.1155/2012/870831
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