一类分数阶随机发展方程非局部问题mild解的存在性  

Existence of mild solutions for a class of fractional stochastic evolution equations with nonlocal initial conditions

作　　者：陈鹏玉 马维凤 Ahmed Abdelmonem CHEN Peng-yu;MA Wei-feng;Ahmed Abdelmonem(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院

出　　处：《山东大学学报（理学版）》2019年第10期13-23,32,共12页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11501455,11661071);西北师范大学研究生培养与课程改革资助项目(2018KGLX01014);“学生创新先锋实验班”资助项目

摘　　要：在非局部函数依赖于未知变量在整个定义区间上的值的情形下,应用随机分析理论、Schauder不动点定理及近似方法,假设非线性函数和非局部项是Carathéodory连续的并且满足较弱增长条件,获得了一类分数阶随机发展方程非局部问题mild解的存在性结果。此工作可以看作是对具有一般非局部初始条件的分数阶发展方程建立解的存在性理论的一种尝试。最后举例说明所得抽象结果在具有非局部积分条件的分数阶随机偏微分方程中的应用。This paper obtains the existence results of mild solutions to a class of fractional stochastic evolution equations with nonlocal conditions by applying stochastic analysis theory, Schauder fixed point theorem and approximation method assumes that the nonlinear term is Carethéodory continuous and satisfies some weak growth condition, the nonlocal term depends on all the value of independent variable on the whole interval and satisfies some weak growth condition. This work may be viewed as an attempt to develop a general existence theory for fractional stochastic evolution equations with general nonlocal conditions. Finally, as a sample of application, the results are applied to a fractional stochastic partial differential equation with nonlocal integral condition.

关 键 词：分数阶随机发展方程 非局部条件 近似方法 紧半群 WIENER过程 

分 类 号：O175.15[理学—数学] O175.29[理学—基础数学]