Existence of nontrivial solutions for a class of nonlinear fractional Schr\"{o}dinger-Poisson system
Received:January 31, 2021  Revised:May 16, 2021
Key Word: fractional Schr\"{o}dinger-Poisson system   nontrivial solution   perturbation method   Moser iterative method
Fund ProjectL:
 Author Name Affiliation Address Peng Zhang School of Math, Dalian University of Technology 大连理工大学应用数学系 Zhiqing Han School of Math, Dalian University of Technology 大连理工大学应用数学系
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This paper is concerned with the following fractional Schr\"{o}dinger-Poisson system: \begin{equation*} \left\{\begin{array}{l} (-\Delta)^su+u+\phi u=\lambda f(u)\ \text {in} \ \mathbb {R}^3, \(-\Delta)^{\alpha}\phi =u^2\ \text {in} \ \mathbb {R}^3\emph{}, \end{array}\right. \end{equation*} 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.