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Open Access Research

A note on the existence and uniqueness of the solutions to SFDES

Yeol JE Cho1, Sever S Dragomir2 and Young-Ho Kim3*

Author Affiliations

1 Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Republic of Korea

2 School of Computer Science and Mathematics, Victoria University of Technology, P.O. Box 14428, MCMC Melbourne, VIC 8001, Australia

3 Department of Mathematics, Changwon National University, Changwon 641-773, Republic of Korea

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Journal of Inequalities and Applications 2012, 2012:126  doi:10.1186/1029-242X-2012-126

Published: 7 June 2012

Abstract

In this paper, we establish a new proof of the existence and uniqueness of solution to stochastic functional differential equations with infinite delay at phase space BC((-∞, 0]: Rd) which denotes the family of bounded continuous Rd-valued functions φ defined on (-∞, 0] with norm ||φ|| = sup-∞ < θ≤0 |φ(θ)|.

Mathematics Subject Classification (2000): 60H05, 60H10.

Keywords:
existence; uniqueness; stochastic functional differential equations; infinite delay.