For EDITORS

For READERS

All Issues

Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
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.