摘要
研究了二阶脉冲随机微分方程积分边值问题解的存在性,将以往所研究的方程的脉冲项和边值条件做了推广,对其限制条件进行了修改。在脉冲项都含有一阶导数以及积分边值条件的情形下,运用CauchySchwarz不等式、Lipschitz条件、鞅不等式和一些随机分析方法给出了解的存在性条件,并通过Lerayschauder定理证明了该类问题解的存在性。最后给出一个实例说明结论的正确性。
The existence of solutions for integral boundary value problems of second-order impulsive stochastic differential equations is studied.The impulsive terms and boundary conditions of the equations studied previously are generalized,and the limiting conditions are modified.In the case that the impulsive terms contain first derivative and integral boundary conditions,the existence conditions of solutions is given by using Cauchy-Schwarz inequalities,Lipschitz conditions,Martingale inequality and some stochastic analysis methods,and the existence of solutions by fixed point theorem is proved.Finally,an example is given to illustrate the correctness of the conclusion.
作者
孙会贤
顾海波
马丽娜
SUN Hui-xian;GU Hai-bo;MA Li-na(College of Mathematical Sciences,Xinjiang Normal University,Urumqi 830017,China)
出处
《滨州学院学报》
2021年第4期41-49,共9页
Journal of Binzhou University
基金
国家自然科学基金项目(11961069,11861068)
新疆优秀青年科技人才培训计划项目(2019Q022)
新疆维吾尔自治区自然科学基金项目(2019D01A71,2018D01A27)
新疆维吾尔自治区高校科研计划项目(XJEDU2018Y033)。
关键词
脉冲随机微分方程
积分边值问题
不动点定理
impulsive stochastic differential equation
integral boundary value problem
fixed point theorem
