  This paper is concerned with the existence of a nonnegative ground state
solution of the following quasilinear Schr\"{o}dinger equation
\begin{equation*} \begin{split}
  -\Delta_{H,p}u+V(x)|u|^{p-2}u-\Delta_{H,p}(|u|^{2\alpha})
|u|^{2\alpha-2}u=\lambda |u|^{q-1}u \text{ in }\;R^n;\;
  u\in W^{1,p}(\;R^n)\cap L^\infty(\;R^N) \end{split} \end{equation*} where
$N\geq2$; $(\alpha,p)\in D_N=\{(x,y)\in \;R^2 : 2xy\geq y+1,\; y\geq2x,\;
y<N\}$ and $\lambda>0$ is a parameter. The operator $\Delta_{H,p}$ is the
reversible Finsler p-Laplacian operator with the function $H$ being the
Minkowski norm on $\;R^N$. Under certain conditions on $V$, we establish the
existence of a non-trivial non-negative bounded ground state solution of the
above equation.
