The present study is concerned with the following fractional Schr\"{ o}dinger-Poisson system with steep potential well: $$ \left\{ % \begin{ array}{ ll} (-\Delta)^s u+ \la V(x)u+K(x)\phi u= f(u), & x\in\R^3, (-\Delta)^t \phi=K(x)u^2, & x\in\R^3, \end{ array}% \right. $$ where $s,t\in(0,1)$ with $4s+2t>3$, and $\la>0$ is a parameter. Under certain assumptions on $V(x)$, $K(x)$ and $f(u)$ behaving like $|u|^{ q-2}u$ with $2<q<2_s^*=\frac{ 6}{ 3-2s}$, the existence of positive ground state solutions and concentration results are obtained via some new analytical skills and Nehair-Poho\v{ z}aev identity. In particular, the monotonicity assumption on the nonlinearity is not necessary.
Categories: math.AP