Existence of Nontrivial Solutions for a Class of Nonlinear Fractional Schr\"{o}dinger-Poisson System
Received:January 31, 2021  Revised:May 20, 2021
Key Word: fractional Schr\"{o}dinger-Poisson system   nontrivial solution   perturbation method   Moser iterative method
Fund ProjectL:
 Author Name Affiliation Peng ZHANG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China Zhiqing HAN School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
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{R}^3\emph{},\end{array}\right. where $s\in (\frac{3}{4},1), \alpha\in(0,1),\lambda$ is a positive parameter, $(-\Delta)^s,(-\Delta)^{\alpha}$ are fractional Laplacian operators. Under certain assumptions on $f$, we obtain the existence of at least one nontrivial solution of the system by using the methods of perturbation and Moser iterative method.