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Existence and Uniqueness of Mild Solutions for Nonlinear Stochastic Impulsive Differential Equation

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  • L. J. Shen
  • J. T. Sun

Abstract

This paper investigates the existence and uniqueness of mild solutions to the general nonlinear stochastic impulsive differential equations. By using Schaefer′s fixed theorem and stochastic analysis technique, we propose sufficient conditions on existence and uniqueness of solution for stochastic differential equations with impulses. An example is also discussed to illustrate the effectiveness of the obtained results.

Suggested Citation

  • L. J. Shen & J. T. Sun, 2011. "Existence and Uniqueness of Mild Solutions for Nonlinear Stochastic Impulsive Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:439724
    DOI: 10.1155/2011/439724
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    References listed on IDEAS

    as
    1. Shiguo Peng & Liping Yang, 2010. "Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Shiguo Peng & Liping Yang, 2010. "Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-11, February.
    3. Mykola Perestyuk & Petro Feketa, 2011. "Invariant Sets of Impulsive Differential Equations with Particularities in ω‐Limit Set," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    4. Mykola Perestyuk & Petro Feketa, 2011. "Invariant Sets of Impulsive Differential Equations with Particularities in ω -Limit Set," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, April.
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