In this paper, we study the following fractional Schrödinger–Poisson system $\left\{\begin{array}{c}{(-\Delta )}^{s}u+V\left(x\right)u+\varphi u=f(x,u)+\lambda {\left|u\right|}^{p-2}u,\text{in}{\mathbb{R}}^3,\hfill \\ {(-\Delta )}^t\varphi =u^2,\text{in}{\mathbb{R}}^3,\hfill \end{array}\right.$where $s\in (\frac{3}{4},1)$, $t\in (0,1)$, $\lambda >0$ is a real parameter, ${(-\Delta )}^s$ is the fractional Laplace operator, $p\ge 2_s^{\ast }=\frac{6}{3-2s}$. Under some suitable assumptions on $V$ and $f$, by using Moser iterative method and truncation technique, we prove that the above equation has a ground state solution and a sign-changing solution.

中文翻译：

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分数薛定ding-泊松系统具有临界或超临界非线性的多种解决方案

在本文中，我们研究以下分数薛定ding－泊松系统 $\left\{\begin{array}{c}{（-\Delta ）}^sü+V（X）ü+\varphi ü=F（X，ü）+\lambda {\left|ü\right|}^{p-2}ü，\text{在}{\mathbb{[R}}^3，\hfill \\ {（-\Delta ）}^{Ť}\varphi ={ü}^2，\text{在}{\mathbb{[R}}^3，\hfill \end{array}\right.$哪里 $s\in （\frac{3}{4}，\mathrm{1个}）$， $Ť\in （0，\mathrm{1个}）$， $\lambda >0$ 是一个实参 ${（-\Delta ）}^s$ 是分数拉普拉斯算子， $p\ge 2_s^{\ast }=\frac{6}{3-2s}$。在一些适当的假设下$V$ 和 $F$通过使用Moser迭代法和截断法，我们证明了上述等式具有基态解和符号转换解。