Title: Ground state sign-changing solutions for a class of nonlinear fractional Schrödinger-Poisson system in $\mathbb{R}^{3}$,
Abstract: In this paper, we are concerned with the existence of the least energy
sign-changing solutions for the following fractional Schrödinger-Poisson
system: \begin{align*}
\left\{ \begin{aligned} &(-\Delta)^{s} u+V(x)u+\lambda\phi(x)u=f(x, u),\quad
&\text{in}\, \ \mathbb{R}^{3},\\ &(-\Delta)^{t}\phi=u^{2},& \text{in}\,\
\mathbb{R}^{3}, \end{aligned} \right. \end{align*} where $\lambda\in
\mathbb{R}^{+}$ is a parameter, $s, t\in (0, 1)$ and $4s+2t>3$, $(-\Delta)^{s}$
stands for the fractional Laplacian. By constraint variational method and
quantitative deformation lemma, we prove that the above problem has one least
energy sign-changing solution. Moreover, for any $\lambda>0$, we show that the
energy of the least energy sign-changing solutions is strictly larger than two
times the ground state energy.
Finally, we consider $\lambda$ as a parameter and study the convergence
property of the least energy sign-changing solutions as $\lambda\searrow 0$.