本文对分数阶拉普拉斯方程一类弱解存在性问题进行讨论，首先通过对一般拉普拉斯方程的弱解存在性问题综述，然后通过对一般拉普拉斯方程的弱解问题进行推广，引入分数阶拉普拉斯方程的一些拓展形式定义及变形公式的具体证明，最后对Lax-Milgram 定理做了一个的推广，然后证明分数阶拉普拉斯方程在周期域上弱解的存在性.

In this article, we will summarize the work of fractional Laplace operator. Firstly, we will discuss the weak solution equation of Laplace and its existence, then we will give the proof of the weak solution of the Laplace equation. Finally, we will introduce the definition of fractional Laplace equation evolution and transformation formula of specific certificate, as well as some famous evidence reviewed in this paper. Lastly, we will prove the existence of the solution of the Laplace equation.