Infinitely many negative energy solutions for fractional Schrödinger–Poisson systems

Abstract

We consider the following fractional Schrödinger–Poisson system $\left(\begin{array}{cc}{(-\Delta )}^{s}u+V\left(x\right)u+\varphi u=f\left(u\right),& \text{in}{R}^3,\\ {(-\Delta )}^s\varphi =u^2,& \text{in}{R}^3,\end{array}\right)$where $s\in (\frac{1}{2},1)$ is a fixed constant, $f$ is continuous, sublinear at the origin and subcritical at infinity. Applying the Clark’s theorem and truncation method, we can obtain a sequence of negative energy solutions.