Ground state and nodal solutions for fractional Schrödinger-Maxwell-Kirchhoff systems with pure critical growth nonlinearity

In this paper, we consider the existence of a ground state nodal solution and solution, energy doubling property asymptotic behavior solutions following fractional critical problem \begin{document}$ \begin{equation*} \begin{cases} (a+ b\int_{\mathbb{R}^{3}}(|(-\Delta)^{\alpha/2}u|^{2})dx)(-\Delta)^{\alpha}u+V(x)u+K(x)\phi u = |u|^{2^{\ast}-2}u+ \kappa f(x,u), (-\Delta)^{\beta}\phi K(x)u^{2}, \quad x\in\mathbb{R}^{3}, \end{cases} \end{equation*} $\end{document} where a, b,\kappa are positive parameters, \alpha\in(\frac{3}{4},1),\beta\in(0,1) , 2^{\ast}_{\alpha} \frac{6}{3-2\alpha} (-\Delta)^{\alpha} stands for Laplacian. By Nehari manifold method, each b>0 obtain u_{b} ground-state v_b to when \kappa\gg 1 nonlinear function f:\mathbb{R}^{3}\times\mathbb{R}\rightarrow\mathbb{R} is Caratheodory function. We also give an analysis on as parameter b\to 0 .