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Existence, uniqueness and stability of the solutions to neutral stochastic founctional differential equations with infinite delay
journal contribution
posted on 2023-05-17, 00:23 authored by Ren, Yong, Xia, NIn 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 ƒÓ defined on (-‡,0] with norm ƒÓ=sup-‡<ƒÆ0|ƒÓ(ƒÆ)| 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.
History
Publication title
Applied Mathematics and ComputationVolume
210Pagination
72-79ISSN
0096-3003Department/School
School of Natural SciencesPublisher
Elsevier Science IncPlace of publication
360 Park Ave South, New York, USA, Ny, 10010-1710Rights statement
The definitive version is available at http://www.sciencedirect.comRepository Status
- Restricted