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Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays

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  • Chen, Huabin

Abstract

In this letter, by establishing an impulsive-integral inequality, some sufficient conditions about the exponential stability in -moment of mild solution for impulsive stochastic partial differential equation with delays are obtained. The results in Caraballo and Liu [Caraballo, T. and Liu, K., 1999a. Exponential stability of mild solutions of stochastic partial differential equations with delays. Stoch. Anal. Appl. 17, 743-763] and Luo [Luo, J., 2008b. Fixed points and exponential stability of mild solutions of stochastic partial differential equation with delays. J. Math. Anal. Appl. 342, 753-760] are generalized and improved.

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  • Chen, Huabin, 2010. "Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 50-56, January.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:1:p:50-56
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    References listed on IDEAS

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    1. Caraballo, Tomás & Liu, Kai, 1999. "On exponential stability criteria of stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 289-301, October.
    2. Liu, Kai & Mao, Xuerong, 1998. "Exponential stability of non-linear stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 173-193, November.
    3. Liu, Kai & Truman, Aubrey, 2000. "A note on almost sure exponential stability for stochastic partial functional differential equations," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 273-278, November.
    4. Wan, Li & Duan, Jinqiao, 2008. "Exponential stability of non-autonomous stochastic partial differential equations with finite memory," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 490-498, April.
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    Cited by:

    1. Li, Dingshi & Fan, Xiaoming, 2017. "Exponential stability of impulsive stochastic partial differential equations with delays," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 185-192.
    2. Huabin Chen, 2015. "The existence and exponential stability for neutral stochastic partial differential equations with infinite delay and poisson jump," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(2), pages 197-217, April.
    3. Long, Shujun & Teng, Lingying & Xu, Daoyi, 2012. "Global attracting set and stability of stochastic neutral partial functional differential equations with impulses," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1699-1709.
    4. Jiang, Feng & Yang, Hua & Shen, Yi, 2016. "A note on exponential stability for second-order neutral stochastic partial differential equations with infinite delays in the presence of impulses," Applied Mathematics and Computation, Elsevier, vol. 287, pages 125-133.
    5. Chen, Guiling & van Gaans, Onno & Lunel, Sjoerd Verduyn, 2018. "Existence and exponential stability of a class of impulsive neutral stochastic partial differential equations with delays and Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 7-18.

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