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Existence of Square‐Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces

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  • Lijie Li

Abstract

The existence and uniqueness of square‐mean almost automorphic mild solution to a stochastic functional integrodifferential equation is studied. Under some appropriate assumptions, the existence and uniqueness of square‐mean almost automorphic mild solution is obtained by Banach’s fixed point theorem. Particularly, based on Schauder’s fixed point theorem, the existence of square‐mean almost automorphic mild solution is obtained by using the condition which is weaker than Lipschitz conditions. Finally, an example illustrating our main result is given.

Suggested Citation

  • Lijie Li, 2014. "Existence of Square‐Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:480241
    DOI: 10.1155/2014/480241
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    References listed on IDEAS

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    1. Gaston M. N’Guerekata, 2001. "Almost Automorphic and Almost Periodic Functions in Abstract Spaces," Springer Books, Springer, number 978-1-4757-4482-8, March.
    2. David N. Keck & Mark A. McKibben, 2005. "Abstract stochastic integrodifferential delay equations," International Journal of Stochastic Analysis, Hindawi, vol. 2005, pages 1-31, January.
    3. 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.
    4. Huang, Zaitang & Yang, Qi-Gui, 2009. "Existence and exponential stability of almost periodic solution for stochastic cellular neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 773-780.
    5. David N. Keck & Mark A. McKibben, 2003. "Functional integro-differential stochastic evolution equations in Hilbert space," International Journal of Stochastic Analysis, Hindawi, vol. 16, pages 1-21, January.
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