In the present paper, we deal with the following Kirchhoff-Schr\”{o}dinger-Poisson system with logarithmic and critical nonlinearity: \begin{equation*} \begin{array}{ll} \left \{ \begin{array}{ll} \ds\B(a+b\int_\Omega|\nabla u|^2\mathrm{d}x \B)\Delta u+V(x)u-\frac{1}{2}u\Delta (u^2)+\phi u=\lambda |u|^{q-2}u\ln|u|^2+|u|^4u, &x\in \Omega, \\ -\Delta \phi=u^2,& x\in \Omega, \\ u=0,& x\in \R^3\setminus\Omega, \end{array} \right . \end{array} \end{equation*} where $\lambda,b>0,a>\frac{1}{4},4

\begin{abstract} {In this paper, we study a class of critical fractional Kirchhoff-type equations involving logarithmic nonlinearity and steep potential well in $\R^N$ as following: \begin{align*} \renewcommand{\arraystretch}{1.25} \begin{array}{ll} \ds \left \{ \begin{array}{ll} \ds \left(a+b\int_{\R^{N}}|(-\Delta)^\frac{s}{2}u|^2\, dx\right)(-\Delta)^s u+\mu V(x)u=\lambda a(x)u\ln|u|+|u|^{2_{s}^{*}-2}u~~~\text{in}~\mathbb{R}^N, \\ u\in H^s(\R^N), \\ \end{array} \right . \end{array} \end{align*} where $a>0$ is a constant, $b$ is a positive parameter, $s\in(0,1)$ and $N>4s,$ $\mu>0$ is a parameter and $V(x)$ satisfies some assumptions that will be specified later. By applying the Nehari manifold method, we obtain that such equation with sign-changing weight potentials admits at least one positive ground state solution and the associated energy is negative. Moreover, we also explore the asymptotic behavior as $b\to 0$ and $\mu\to\infty,$ respectively.}

{We study the existence and asymptotic behavior of positive solutions for the following fractional magnetic Kirchhoff equation with steep potential well \begin{align*} \renewcommand{\arraystretch}{1.25} \begin{array}{ll} \ds \left \{ \begin{array}{ll} \ds \left(a+b\int_{\R^{3}}|(-\Delta)_A^\frac{s}{2}u|^2\, dx\right)(-\Delta)_A^s u+V_{\lambda}u=|u|^{p-2}u~~~in~\mathbb{R}^3, \\ u\in H^s(\R^3), \\ \end{array} \right . \end{array} \end{align*} where $a,~b>0$ are constants, $2

\begin{abstract} {In this paper we consider the following fractional Kirchhoff equation with steep potential well \begin{align*} \renewcommand{\arraystretch}{1.25} \begin{array}{ll} \ds \left \{ \begin{array}{ll} \ds \left(a+b\int_{\R^{3}}|(-\Delta)^\frac{s}{2}u|^2\, dx\right)(-\Delta)^s u+\lambda V(x)u=|u|^{p-2}u,\,\,x\in\mathbb{R}^3, \\ u\in H^s(\R^3), \\ \end{array} \right . \end{array} \end{align*} where $a>0$ is a constant, $b$ and $\lambda$ are positive parameters. $2