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The present study is concerned with the following Schr\"{o}dinger-Poissonsystem involving critical nonlocal term with general nonlinearity: $$ \left\{\begin{array}{ll} -\Delta u+V(x)u- \phi |u|^3u= f(u), & x\in\mathbb{R}^3,-\Delta \phi= |u|^5, & x\in\mathbb{R}^3,\\ \end{array} \right. $$ Under certainassumptions on non-constant $V(x)$, the existence of a positive least energysolution is obtained by using some new analytical skills and Poho\v{z}aev typemanifold. In particular, the Ambrosetti-Rabinowitz type condition ormonotonicity assumption on the nonlinearity is not necessary.

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