Abstract:

This paper studies the following fourth order quasilinear elliptic equation

\begin{equation*}

\left\{\begin{aligned}

&\triangle^{2} u-\triangle u+V(x)u-\frac{1}{2}u\triangle (u^{2})=f(u),&x\in \mathbb{R}^{N},\\

&u\in H^{2}(\mathbb{R}^{N}),

\end{aligned}

\right.

\end{equation*}

where $\triangle^{2}:=\triangle(\triangle)$ is the biharmonic operator, $2<N\leq 6$. We prove that the equation admits a ground state solution of the Nehari-Poho\u{z}aev type.

Key words: Fourth order quasilinear elliptic equation, Ground state solution of\ Nehari-Poho\u{z}aev type,  , Variational method