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A note on the existence and uniqueness of mild solutions to neutral stochastic partial functional differential equations with non-Lipschitz coefficients. (English) Zbl 1217.60054

Summary: We study the existence and uniqueness of mild solutions to neutral stochastic partial functional differential equations under some Carathéodory-type conditions on the coefficients by means of the successive approximation. In particular, we generalize and improve the results of T.E. Govindan [Stochastics 77, No. 2, 139–154 (2005; Zbl 1115.60064)] and J. Bao and Z. Hou [Comput. Math. Appl. 59, No. 1, 207–214 (2010; Zbl 1189.60122)].

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R10 Partial functional-differential equations
35R60 PDEs with randomness, stochastic partial differential equations
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References:

[1] Liu, K., Stability of Infinite Dimensional Stochastic Differential Equations with Applications (2006), Chapman and Hall, CRC: Chapman and Hall, CRC London
[2] Govindan, T. E., Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics, 77, 139-154 (2005) · Zbl 1115.60064
[3] Bao, J.; Hou, Z., Existence of mild solutions to stochastic neutral partial functional differential equations with non-Lipschitz coefficients, Comput. Math. Appl., 59, 207-214 (2010) · Zbl 1189.60122
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