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Volume 9, Number 3, 2019, Pages 1165-1182                                                                DOI:10.11948/2156-907X.20190022
Infinitely many solutions for fractional Schrodinger-Maxwell equations
Jiafa Xu,Zhongli Wei,Donal O Regan,Donal O''Regan,Yujun Cui
Keywords:Fractional Laplacian, Schrodinger-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.
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