Multiple positive solutions for Schrodinger-Poisson systems involving critical nonlocal term

The present study is concerned with the following Schr"{o}dinger-Poisson system involving critical nonlocal term $$\{\begin{array}{lll}-\mathrm{\Delta }u+u-K(x)\varphi \mathrm{\mid }u{\mathrm{\mid }}^{3}u=\lambda f(x)\mathrm{\mid }u{\mathrm{\mid }}^{q-2}u,& x\in {\mathbb{R}}^3,-\mathrm{\Delta }\varphi =K(x)\mathrm{\mid }u{\mathrm{\mid }}^5,& x\in {\mathbb{R}}^3,\end{array}$$ where $1<q<2$ and $\lambda >0$ is a parameter. Under suitable assumptions on $K(x)$ and $f(x)$, there exists ${\lambda }_0={\lambda }_0(q,S,f,K)>0$ such that for any $\lambda \in (0,{\lambda }_0)$, the above Schr"{o}dinger-Poisson system possesses at least two positive solutions by standard variational method, where a positive least energy solution will also be obtained.