Hilbert空间上无穷时滞中立型随机偏泛函微分方程适度解的存在唯一性

Existence and Uniqueness of Mild Solution to Neutral Stochastic Partial Functional Differential Equations with Infinite Delay in Hilbert Spaces

首先给出了Hilbert空间上无穷时滞中立型随机偏泛函微分方程适度解的定义,然后利用解析半群的性质,Burkholder-Davis-Gundy不等式和Banach不动点定理证明了该Hilbert空间上无穷时滞中立型随机偏泛函微分方程适度解的存在唯一性,最后举出一个实例说明了所得结果的有效性。

Firstly,the definition of the mild solution to neutral stochastic partial functional differential equations with infinite delay in Hilbert spaces was introduced.Then,by means of the properties of analytic semigroups,Burkholder-Davis-Gundy inequality,and Banach fixed point theorem,the existence and uniqueness of the mild solution to neutral stochastic partial functional differential equations with infinite delay in Hilbert spaces were obtained.Finally,an example was given to illustrate the results.