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Ground state for fractional Schrödinger-Poisson equation in Coulomb-Sobolev space

  • * Corresponding author: Dun Zhao

    * Corresponding author: Dun Zhao
This work is supported by NSFC under Grant No. 12075102 and 11971212
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  • We consider the following fractional Schrödinger-Poisson equation with combined nonlinearities

    $ \begin{equation*} \begin{cases} (-\Delta)^su+\phi u = |u|^{s^*-2}u+\mu|u|^{p-2}u \,\,\,\rm{in}\ \mathbb{R}^3,\\ -\Delta \phi = 4\pi u^2\ \rm{in}\ \mathbb{R}^3, \end{cases} \end{equation*} $

    where $ s\in(\frac{3}{4},1) $, $ \mu>0 $, $ p\in(3,s^*) $ and $ s^* = \frac{6}{3-2s} $. By the perturbation approach we prove the existence of the ground state solution in fractional Coulomb-Sobolev space.

    Mathematics Subject Classification: Primary: 35A15, 35Q55, 35R11; Secondary: 35Q40.


    \begin{equation} \\ \end{equation}
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