文献类型：期刊文献

英文题名：Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay

作者：Ren, Yong[1];Lu, Shiping[1];Xia, Ningmao[2]

机构：[1]Anhui Normal Univ, Dept Math, Wuhu 241000, Peoples R China;[2]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2008

卷号：220

期号：1-2

起止页码：364

外文期刊名：JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

收录：;EI(收录号：20083111416591);WOS:【SCI-EXPANDED(收录号:WOS:000258636800030)】；

基金：The authors wish to thank the anonymous referee for his or her valuable comments, correcting errors and improving written language. And the work was supported by the Key Science and Technology Project of Ministry of Educational (China 207047).

语种：英文

外文关键词：stochastic functional differential equations; infinite delay; existence; uniqueness

摘要：In this paper, we obtain some results on the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay at phase space BC((-infinity. 0 vertical bar; R-d) which denotes the family of bounded continuous R-d-value functions phi defined on (-infinity. 0 vertical bar with norm parallel to phi parallel to = sup(-infinity < 0 <= 0) vertical bar phi (0)vertical bar 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. (c) 2007 Elsevier B.V. All rights reserved.