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随机Volterra-Levin方程解的存在唯一性与稳定性
引用本文:郭利芳,朱全新. 随机Volterra-Levin方程解的存在唯一性与稳定性[J]. 宁波大学学报(理工版), 2011, 24(4): 56-59
作者姓名:郭利芳  朱全新
作者单位:宁波大学理学院,浙江宁波,315211
基金项目:国家自然科学基金,宁波市自然科学基金
摘    要:应用逐次逼近法研究了随机Volterra—Levin方程解的存在性,并结合H61der不等式证明了该方程解的唯一性与稳定性.最后用2个例子说明所获结果的有效性,同时表明条件“存在常数m〉0,使得∫-L^0p(s)ds=m”和“对所有的t≥0,∫0^1 e^4amsσ^2(t)ds/e^4amt都有界”是对Luo提出的条件进行了改进.

关 键 词:逐次逼近法  随机Volterra-Levin方程  存在性  唯一性  稳定性

Existence, Uniqueness and Stability of Stochastic Volterra-Levin Equation
GUO Li-fang,ZHU Quan-xin. Existence, Uniqueness and Stability of Stochastic Volterra-Levin Equation[J]. Journal of Ningbo University(Natural Science and Engineering Edition), 2011, 24(4): 56-59
Authors:GUO Li-fang  ZHU Quan-xin
Affiliation:GUO Li-fang,ZHU Quan-xin(Faculty of Science,Ningbo University,Ningbo 315211,China)
Abstract:Using the method of successive approximations, the existence of the solution for stochastic Volterra-Levin equations is obtained. Also, based on the H61der inequality, the solution is proven unique and stable. Finally, two examples show that the proposed conditions "there exists a constant m 〉 0, such that ∫-L^0p(s)ds=m" and "t≥0,∫0^1 e^4amsσ^2(t)ds/e^4amt is bounded for all t≥0"generalize and improve those given in Luo's paper.
Keywords:successive approximations  stochastic Volterra-Levin equations  existence  uniqueness  stability
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