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Infinitely many solutions for fractional Schrödinger-Poisson systems with sign-changing potential. (English) Zbl 1370.35116

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.

MSC:

35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
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