Ground state for fractional Schrödinger-Poisson equation in Coulomb-Sobolev space
Ground state for fractional Schrödinger-Poisson equation in Coulomb-Sobolev space
<p style='text-indent:20px;'>We consider the following fractional Schrödinger-Poisson equation with combined nonlinearities <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \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*} $\end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ s\in(\frac{3}{4},1) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ \mu>0 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ p\in(3,s^*) $\end{document}</tex-math></inline-formula> …