Nehari-type ground state solutions for asymptotically periodic bi-harmonic Kirchhoff-type problems in ${\mathbb{R}}^N$

We investigate the following Kirchhoff-type biharmonic equation \begin{equation}\label{pr} \left{ \begin{array}{ll} Δ^2 u+ \left(a+b\int_{$\mathbb{R}$^N}|\nabla u|^2d x\right)(-Δu+V(x)u)=f(x,u),\quad x\in $\mathbb{R}$^N,\ u\in H^{2}($\mathbb{R}$^N), \end{array} \right. \end{equation} where $a>0$, $b\ge 0$ and $V(x)$ and $f(x,u)$ are periodic or asymptotically periodic in $x$. We study the existence of Nehari-type ground state solutions of the problem just above with $f(x,u)u-4F(x,u)$ sign-changing, where $F(x,u):={\int }_0^{u}f(x,s)ds$. We significantly extend some results from the previous literature.