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Existence, uniqueness and stability of the solutions to neutral stochastic founctional differential equations with infinite delay

Citation

Ren, Yong and Xia, N, Existence, uniqueness and stability of the solutions to neutral stochastic founctional differential equations with infinite delay, Applied Mathematics and Computation, 210, (1) pp. 72-79. ISSN 0096-3003 (2009) [Refereed Article]


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DOI: doi:10.1016/j.amc.2008.11.009

Abstract

In this paper, we obtain the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay at phase space BC((-,0];Rd) which denotes the family of bounded continuous Rd- value functions defined on (-,0] with norm =sup-<0|()| under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition. The solution is constructed by the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial value by means of the Corollary of Bihari inequality.

Item Details

Item Type:Refereed Article
Keywords:Neutral stochastic functional differential, equations, Infinite delay, Picard approximation
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Partial Differential Equations
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Ren, Yong (Dr Yong Ren)
ID Code:58476
Year Published:2009
Web of Science® Times Cited:47
Deposited By:Mathematics
Deposited On:2009-10-08
Last Modified:2010-03-25
Downloads:0

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