Global attracting set and stability of stochastic neutral partial functional differential equations with impulses
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.
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Volume (Year): 82 (2012)
Issue (Month): 9 ()
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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.
- 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.
- Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
- 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.
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