@Article{ Shao2018, author="Liuyang Shao, Haibo Chen", title="Ground states solutions for modified fourth-order elliptic systems with steep well potential", year="2018", volume="11", number="3", pages="323--334", abstract="In this paper, we study the following modified quasilinear fourth-order elliptic systems \[ \left\{\begin{array}{lll} \triangle^{2}u-\triangle u+(\lambda\alpha(x)+1)u-\frac{1}{2}\triangle(u^{2})u=\frac{p}{p+q}|u|^{p-2}|v|^{q}u,~~ \mbox{in} \;~\mathbb{R}^{N}, \\ \triangle^{2}v-\triangle v+(\lambda\beta(x)+1)v-\frac{1}{2}\triangle(v^{2})v=\frac{q}{p+q}|u|^{p}|v|^{q-2}v,~~ \mbox{in} \;~\mathbb{R}^{N},\end{array} \right.\] where \(\triangle^{2}=\triangle(\triangle)\) is the biharmonic operator, \(\lambda>0\), and \(2