Title: The existence of positive least energy solutions for a class of Schrodinger-Poisson systems involving critical nonlocal term with general nonlinearity,
Abstract: The present study is concerned with the following Schrödinger-Poisson
system 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 certain
assumptions on non-constant $V(x)$, the existence of a positive least energy
solution is obtained by using some new analytical skills and Pohožaev type
manifold. In particular, the Ambrosetti-Rabinowitz type condition or
monotonicity assumption on the nonlinearity is not necessary.