The existence of positive least energy solutions for a class of Schrodinger-Poisson systems involving critical nonlocal term with general nonlinearity

The present study is concerned with the following Schr"{o}dinger-Poisson system involving critical nonlocal term with general nonlinearity: $$\{\begin{array}{lll}-\mathrm{\Delta }u+V(x)u-\varphi \mathrm{\mid }u{\mathrm{\mid }}^{3}u=f(u),& x\in {\mathbb{R}}^3,-\mathrm{\Delta }\varphi =\mathrm{\mid }u{\mathrm{\mid }}^5,& x\in {\mathbb{R}}^3,\end{array}$$ Under certain assumptions on non-constant $V(x)$, the existence of a positive least energy solution is obtained by using some new analytical skills and Poho\v{z}aev type manifold. In particular, the Ambrosetti-Rabinowitz type condition or monotonicity assumption on the nonlinearity is not necessary.