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Existence of mild solutions to stochastic neutral partial functional differential equations with non-Lipschitz coefficients. (English) Zbl 1189.60122
Summary: Under a non-Lipschitz condition with the Lipschitz condition being considered as a special case and a weakened linear growth condition, the existence and uniqueness of mild solutions to stochastic neutral partial functional differential equations (SNPFDEs) is investigated. Some results of T. E. Govindan [Stochastic Anal. Appl. 21, No. 5, 1059–1077 (2003; Zbl 1036.60052); Stochastics 77, No. 2, 139–154 (2005; Zbl 1115.60064)] are generalized to cover a class of more general SNPFDEs.

60H15Stochastic partial differential equations
35R10Partial functional-differential equations
35R60PDEs with randomness, stochastic PDE
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