Abstract
In this paper, we consider the stability in pth moment of mild solutions to nonlinear impulsive stochastic delay partial differential equations (NISDPDEs). By employing a fixed point approach, sufficient conditions for the exponential stability in pth moment of mild solutions are derived.
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Liu, K.: Stability of Infinite Dimensional Stochastic Differential Equations with Applications. Chapman and Hall, CRC, London (2006)
Luo, J., Liu, K.: Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps. Stochastic Process. Appl. 118, 864–895 (2008)
Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Cambridge University Press (1992)
Taniguchi, T.: The existence and asymptotic behavior of mild solutions to stochastic evolution equations with infinite delays driven by Poisson jumps. Stoch. Dyn. 9, 217–229 (2009)
Wan, L., Duan, J.: Exponential stability of non-autonomous stochastic partial differential equations with finite memory. Statist. Probab. Lett. 78, 490–498 (2008)
Luo, J.: Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays. J. Math. Anal. Appl. 342, 753–760 (2008)
Burton, T.A.: Stability by fixed point theory or Lyapunov theory: a comparison. Fixed Point Theory 4, 15–32 (2003)
Burton, T.A.: Fixed points, stability and exact linearization. Nonlinear Anal. 61, 857–870 (2005)
Burton, T.A., Furumochi, T.: Asymptotic behavior of solutions of functional differential equations by fixed point theorems. Dynam. Systems Appl. 11, 499–521 (2002)
Burton, T.A., Zhang, B.: Fixed points and stability of an integral equation: nonuniqueness. Appl. Math. Lett. 17, 839–846 (2004)
Luo, J., Taniguchi, T.: Fixed points and stability of stochastic neutral partial differential equations with infinite delay. Stoch. Anal. Appl. 27(6), 1163–1173 (2009)
Wu, S.L., Li, K.L., Zhang, J.S.: Exponential stability of discrete-time neural networks with delay and impulses. Appl. Math. Comput. 218(12), 6972–6986 (2012)
Zhang, X.M., Huang, X.Y., Liu, Z.H.: The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay. Nonlinear Analysis: Hybrid Sys. 4(4), 775–781 (2010)
Cui, J., Yan, L.T.: Existence results for impulsive neutral second-order stochastic evolution equations with nonlocal conditions. Math. Comput. Model. (in press, 2012)
Lin, A.H., Ren, Y., Xia, N.M.: On neutral impulsive stochastic integro-differential equations with infinite delays via fractional operators. Math. Comput. Model. 51, 413–424 (2010)
Tai, Z.X., Lun, S.X.: On controllability of fractional impulsive neutral infinite delay evolution integrodifferential systems in Banach spaces. Appl. Math. Lett. 25(2), 104–110 (2012)
Liu, K.: Lyapunov functionals and asymptotic stability of stochastic delay evolution equations. Stochastics 63, 1–26 (1998)
Taniguchi, T.: The exponential stability for stochastic delay partial differential equations. J. Math. Anal. Appl. 331, 191–205 (2007)
Hou, Z., Bao, J., Yuan, C.: Exponential stability of energy solutions to stochastic partial differential equations with variable delay and jumps. J. Math. Anal. Appl. 366, 44–54 (2010)
Liu, K., Truman, A.: A note on almost sure exponential stability for stochastic partial functional differential equations. Statist. Probab. Lett. 50(3), 273–278 (2000)
Luo, J.: Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays. J. Math. Anal. Appl. 342, 753–760 (2008)
Luo, J., Liu, K.: Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps. Stochastic Process. Appl. 118, 864–895 (2008)
Samidurai, R., Anthoni, S.M., Balachandran, K.: Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays. Nonlinear Analysis: Hybrid Sys. 4(4), 103–112 (2010)
Sakthivel, R., Luo, J.: Asymptotic stability of impulsive stochastic partial differential equations with infinite delays. J. Math. Anal. Appl. 356, 1–6 (2009)
Taniguchi, T.: Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces. Stochastics 53, 41–52 (1995)
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Zhang, L., Ding, Y., Wang, T., Hu, L., Hao, K. (2012). Moment Exponential Stability of Neutral Impulsive Nonlinear Stochastic Delay Partial Differential Equations. In: Xiao, T., Zhang, L., Fei, M. (eds) AsiaSim 2012. AsiaSim 2012. Communications in Computer and Information Science, vol 323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34384-1_38
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DOI: https://doi.org/10.1007/978-3-642-34384-1_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34383-4
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