### For REFEREES

 Infinitely many solutions for fractional Schr\"{o}dinger-Maxwell equations Jiafa Xu,Zhongli Wei,Donal O''Regan,Yujun Cui Keywords:Fractional Laplacian, Schr\"{o}dinger-Maxwell equations, Infinitely many solutions. Abstract: In this paper using fountain theorems we study the existence of infinitely many solutions for fractional Schr\"{o}dinger-Maxwell equations $\begin{cases} (-\Delta)^\alpha u+\lambda V(x)u+\phi u=f(x,u)-\mu g(x)|u|^{q-2}u, \text{ in } \mathbb R^3,\\ (-\Delta)^\alpha \phi=K_\alpha u^2, \text{ in } \mathbb R^3, \end{cases}$where $\lambda,\mu >0$ are two parameters, $\alpha\in (0,1]$, $K_\alpha=\frac{\pi^{-\alpha}\Gamma(\alpha)}{\pi^{-(3-2\alpha)/2}\Gamma((3-2\alpha)/2)}$ and $(-\Delta)^\alpha$ is the fractional Laplacian. Under appropriate assumptions on $f$ and $g$ we obtain an existence theorem for this system.