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| \ In this paper, we consider the existence of ground state solution and ground state sign-changing solution for the quasilinear Schr\"{o}dinger equation\begin{eqnarray}\label{1.1}-\triangle u-a(x)\triangle (u^2)u+V(x)u=f(x,u) &x\in \mathbb{R}^N\nonumber\end{eqnarray}where $N\geq3$, $V$ is coercive potential, $a(x)$ is a bounded function and $f\in C(\mathbb{R}^N\times\mathbb{R},\mathbb{R})$. The proof is based on variational methods, by using sign-changing Nehari manifold and deformation arguments, we can get a least energy sign-changing solution. |
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| Keywords:Fundamental Mathematics, Quasilinear Schr\"{o}dinger equation, Sign-changing solution\par |
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