The existence of ground state solutions for generalized quasilinear Schrödinger equations

In this paper, we study thefollowing generalized quasilinear Schrodinger equationsbeginalign*-textdivg²(u)∇ u)+g(u)g(u)∇ u²+V(x)u=h(u), x∈ R^N, endalign*where $N\ge~3,~$ $~g:\R\rightarrow\R^+$ is an even differentialfunction satisfying $~\lim_{t~\rightarrow~+\infty}\frac~{g(t)}{t^{\alpha~-1}}=~\beta~>0$ for some $\alpha~\ge~1$;$h:\R\rightarrow[0,+\infty)$ is a nonlinear function covering the case: $h(t)=|t|^{p-2}t$ $~(2