IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v82y2012i9p1699-1709.html
   My bibliography  Save this article

Global attracting set and stability of stochastic neutral partial functional differential equations with impulses

Author

Listed:
  • Long, Shujun
  • Teng, Lingying
  • Xu, Daoyi

Abstract

In this paper, a class of stochastic neutral partial functional differential equations with impulses is investigated. To this end, we first establish a new impulsive-integral inequality, which improve the inequality established by Chen [Chen, H.B., 2010. Impulsive-integral inequality and exponential stability for stochastic partial differential equation with delays. Statist. Probab. Lett. 80, 50–56]. By using the new inequality, we obtain the global attracting set of stochastic neutral partial functional differential equations with impulses. Especially, the sufficient conditions ensuring the exponential p-stability of the mild solution of the considered equations are obtained. Our results can generalize and improve the existing works. An example is given to demonstrate the main results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:9:p:1699-1709
    DOI: 10.1016/j.spl.2012.05.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212001939
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2012.05.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    2. 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.
    3. 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.
    4. Cui, Jing & Yan, Litan & Sun, Xichao, 2011. "Exponential stability for neutral stochastic partial differential equations with delays and Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1970-1977.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. 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.
    4. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    5. Singh, Ajeet & Shukla, Anurag & Vijayakumar, V. & Udhayakumar, R., 2021. "Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. 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.
    7. Alka Chadha & Dwijendra N. Pandey, 2018. "Approximate Controllability of a Neutral Stochastic Fractional Integro-Differential Inclusion with Nonlocal Conditions," Journal of Theoretical Probability, Springer, vol. 31(2), pages 705-740, June.
    8. Cheng, Pei & Deng, Feiqi, 2010. "Global exponential stability of impulsive stochastic functional differential systems," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1854-1862, December.
    9. Peng, Shiguo & Jia, Baoguo, 2010. "Some criteria on pth moment stability of impulsive stochastic functional differential equations," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1085-1092, July.
    10. Kao, Yonggui & Zhu, Quanxin & Qi, Wenhai, 2015. "Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 795-804.
    11. 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.
    12. Lei Zhang & Yongsheng Ding & Kuangrong Hao & Liangjian Hu & Tong Wang, 2014. "Moment stability of fractional stochastic evolution equations with Poisson jumps," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1539-1547, July.
    13. Li, Guangjie & Yang, Qigui, 2021. "Stability analysis of the θ-method for hybrid neutral stochastic functional differential equations with jumps," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    14. Tamilalagan, P. & Balasubramaniam, P., 2017. "Moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 299-307.
    15. Yao, Fengqi & Deng, Feiqi, 2012. "Exponential stability in terms of two measures of impulsive stochastic functional differential systems via comparison principle," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1151-1159.
    16. Cui, Jing & Yan, Litan & Sun, Xichao, 2011. "Exponential stability for neutral stochastic partial differential equations with delays and Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1970-1977.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:82:y:2012:i:9:p:1699-1709. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.