Jiang, Feng; Shen, Yi 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 Comput. Math. Appl. 61, No. 6, 1590-1594 (2011). 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)]. Cited in 1 ReviewCited in 22 Documents MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35R10 Partial functional-differential equations 35R60 PDEs with randomness, stochastic partial differential equations Keywords:Carathéodory condition; non-Lipschitz condition; mild solution; neutral stochastic partial functional differential equations Citations:Zbl 1115.60064; Zbl 1189.60122 PDFBibTeX XMLCite \textit{F. Jiang} and \textit{Y. Shen}, Comput. Math. Appl. 61, No. 6, 1590--1594 (2011; Zbl 1217.60054) Full Text: DOI 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 [4] Taniguchi, T., Successive approximations to solutions of stochastic differential equations, J. Differential Equations, 96, 152-169 (1992) · Zbl 0744.34052 [5] Turo, J., Successive approximations of solutions to stochastic functional differential equations, Period. Math. Hungar., 30, 87-96 (1995) · Zbl 0816.60055 [6] Cao, G.; He, K.; Zhang, X., Successive approximations of infinite dimensional SDES with jump, Stoch. Syst., 5, 609-619 (2005) · Zbl 1082.60048 [7] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations (1992), Springer-Verlag: Springer-Verlag New York · Zbl 0516.47023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.