Chen, Jianhua; Tang, Xianhua; Luo, Huxiao Infinitely many solutions for fractional Schrödinger-Poisson systems with sign-changing potential. (English) Zbl 1370.35116 Electron. J. Differ. Equ. 2017, Paper No. 97, 13 p. (2017). Summary: In this article, we prove the existence of multiple solutions for following fractional Schrodinger-Poisson system with sign-changing potential \[ \begin{aligned} (-\Delta)^s u+V(x)u+\lambda\phi u=f(x,u),\quad x\in\mathbb{R}^3,\\(-\Delta)^t\phi=u^2,\quad x\in\mathbb{R}^3,\end{aligned} \] where \((-\Delta)^\alpha\) denotes the fractional Laplacian of order \(\alpha\in(0,1)\), and the potential \(V\) is allowed to be sign-changing. Under certain assumptions on \(f\), we obtain infinitely many solutions for this system. Cited in 4 Documents MSC: 35J60 Nonlinear elliptic equations 35J20 Variational methods for second-order elliptic equations Keywords:fractional Schrödinger-Poisson systems; sign-changing potential; symmetric mountain pass theorem; infinitely many solutions PDFBibTeX XMLCite \textit{J. Chen} et al., Electron. J. Differ. Equ. 2017, Paper No. 97, 13 p. (2017; Zbl 1370.35116) Full Text: Link