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《微分方程年刊(英文版)》 2014-01
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Daoyi Xu;Bing Li;Shujun Long;Lingying Teng;Weisong Zhou;Yangtze Center of Math.,Sichuan University;College of Science,Chongqing Jiaotong University;College of Math.and Information Science,Leshan Normal University;College of Computer Science and Tech.,Southwest University for Nationalities;  
In this paper,we show the existence and uniqueness of solutions to a large class of SFDEs with the generalized local Lipschitzian coefficients.Some moment estimates of the solutions are given by establishing new It?o operator inequalities based on the Razumikhin technique.These estimates improve,extend and unify some related results including exponential stability of Mao(1997) [20],decay stability of Wu et al.(2010,2011) [32,33],Pavlovic et al.(2012) [24],asymptotic behavior of Luo et al.(2011) [18] and Song et al.(2013) [26].Moreover,stochastic version of Wintner theorem in continuous space is established by the comparison principle,which improve and extend the main results of Xu et al.(2008 [39],2013 [36]).When the methods presented are applied to the SFDEs with impulses and SFDEs in Hilbert spaces,we extend the related results of Govindana et al.(2013) [7],Liu et al.(2007) [15],Vinodkumar(2010) [29] and Xu et al.(2012) [35].Two examples are provided to illustrate the effectiveness of our results.
【Fund】: supported by National Natural Science Foundation of China under Grant 11271270;; Fundamental Research Funds for the Central Universities under Grant 13NZYBS07
【CateGory Index】: O211.63
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