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Sakthivel, R.; Luo, J.

Asymptotic stability of impulsive stochastic partial differential equations with infinite delays. (English) Zbl 1166.60037

J. Math. Anal. Appl. 356, No. 1, 1-6 (2009).
Summary: We study the existence and asymptotic stability in \(p\)th moment of mild solutions to nonlinear impulsive stochastic partial differential equations with infinite delay. By employing a fixed point approach, sufficient conditions are derived for achieving the required result. These conditions do not require the monotone decreasing behaviour of the delays.

Cited in 100 Documents

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

asymptotic stability; mild solution; impulsive stochastic equations; infinite delay
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\textit{R. Sakthivel} and \textit{J. Luo}, J. Math. Anal. Appl. 356, No. 1, 1--6 (2009; Zbl 1166.60037)
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References:

[1] Caraballo, T., Asymptotic exponential stability of stochastic partial differential equations with delay, Stochastics, 33, 27-47, (1990) · Zbl 0723.60074
[2] Caraballo, T.; Liu, K., Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. anal. appl., 17, 743-763, (1999) · Zbl 0943.60050
[3] Caraballo, T.; Real, J., Partial differential equations with delayed random perturbations: existence, uniqueness and stability of solutions, Stoch. anal. appl., 11, 497-511, (1993) · Zbl 0790.60054
[4] Da Prato, G.; Zabczyk, J., Stochastic equations in infinite dimensions, (1992), Cambridge University Press Cambridge · Zbl 0761.60052
[5] Govindan, T.E., Exponential stability in Mean-square of parabolic quasilinear stochastic delay evolution equations, Stoch. anal. appl., 17, 443-461, (1999) · Zbl 0940.60076
[6] Ichikawa, A., Stability of semilinear stochastic evolution equations, J. math. anal. appl., 90, 12-44, (1982) · Zbl 0497.93055
[7] Keck, D.N.; McKibben, M.A., Abstract semilinear stochastic ito – volterra integrodifferential equations, J. appl. math. stoch. anal., 1-22, (2006) · Zbl 1234.60065
[8] Khas’minskii, R., Stochastic stability of differential equations, (1980), Sijthoff & Noordhoff Netherlands · Zbl 0441.60060
[9] Liu, K., Lyapunov functionals and asymptotic stability of stochastic delay evolution equations, Stochastics, 63, 1-26, (1998) · Zbl 0947.93037
[10] Liu, K.; Mao, X., Exponential stability of non-linear stochastic evolution equations, Stochastic process. appl., 78, 173-193, (1998) · Zbl 0933.60072
[11] Liu, K.; Truman, A., A note on almost exponential stability for stochastic partial differential equations, Statist. probab. lett., 50, 273-278, (2000) · Zbl 0966.60059
[12] Liu, K., Stability of infinite dimensional stochastic differential equations with applications, (2006), Chapman & Hall, CRC London
[13] 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) · Zbl 1157.60065
[14] Mao, X., Stochastic differential equations and applications, (1997), Horwood Chichestic, UK · Zbl 0874.60050
[15] Mao, X., Exponential stability of stochastic differential equations, (1994), Marcel Dekker New York · Zbl 0851.93074
[16] Nieto, J.J.; Rodriguez-Lopez, R., Boundary value problems for a class of impulsive functional equations, Comput. math. appl., 55, 2715-2731, (2008) · Zbl 1142.34362
[17] Nieto, J.J.; Rodriguez-Lopez, R., New comparison results for impulsive integro-differential equations and applications, J. math. anal. appl., 328, 1343-1368, (2007) · Zbl 1113.45007
[18] Samoilenko, A.M.; Perestyuk, N.A., Impulsive differential equations, (1995), World Scientific Singapore · Zbl 0837.34003
[19] Taniguchi, T., The exponential stability for stochastic delay partial differential equations, J. math. anal. appl., 331, 191-205, (2007) · Zbl 1125.60063
[20] Taniguchi, T., Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces, Stochastics, 53, 41-52, (1995) · Zbl 0854.60051
[21] Taniguchi, T.; Liu, K.; Truman, A., Existence, uniqueness, and asymptotic behavior of mild solution to stochastic functional differential equations in Hilbert spaces, J. differential equations, 18, 72-91, (2002) · Zbl 1009.34074
[22] Wan, L.; Duan, J., Exponential stability of non-autonomous stochastic partial differential equations with finite memory, Statist. probab. lett., 78, 490-498, (2008) · Zbl 1141.37030
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