This paper deals with a class of nonlocal Schrodinger equations with critical exponent $$\begin{aligned} \left\{ \begin{array}{llll} (-\Delta )^{s} u+V(x)u-K(x)\phi |u|^{2^*_s-3}u=f(x,u),&{}\quad \mathrm{in}\ \mathbb {R}^3,\\ (-\Delta )^s \phi =K(x)|u|^{2^*_s-1},&{}\quad \mathrm{in}\ \mathbb {R}^3. \end{array}\right. \end{aligned}$$ By employing the mountain pass theorem, concentration-compactness principle and approximation method, the existence of nontrivial solution is obtained under appropriate assumptions on V, K and f.

中文翻译：

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包含具有临界指数的分数拉普拉斯算子的薛定谔-泊松方程的非平凡解

本文涉及一类具有临界指数的非局部薛定谔方程 $$\begin{aligned} \left\{ \begin{array}{llll} (-\Delta )^{s} u+V(x)uK(x )\phi |u|^{2^*_s-3}u=f(x,u),&{}\quad \mathrm{in}\ \mathbb {R}^3,\\ (-\Delta ) ^s \phi =K(x)|u|^{2^*_s-1},&{}\quad \mathrm{in}\ \mathbb {R}^3。\end{数组}\对。\end{aligned}$$ 通过采用山口定理、集中紧致原理和近似方法，在对V、K和f的适当假设下获得非平凡解的存在性。