In this paper, we study the existence of a positive ground state solution for a class of generalized quasilinear Schrödinger equations with asymptotically periodic potential. By the variational method, a positive ground state solution is obtained. Compared with the existing results, our results improve and generalize some existing related results.

In this paper, we are concerned with the existence of nontrivial positive solutions for the following generalized quasilinear elliptic equations with critical growth

$$-\mathrm{d}\mathrm{i}\mathrm{v}(g^p(u)|\mathrm{\nabla }u{|}^{p-2}\mathrm{\nabla }u)+g^{p-1}(u)g^{\prime }(u)|\mathrm{\nabla }u{|}^p+V(x)|u{|}^{p-2}u=h(x,u),x\in {\mathbb{R}}^N,$$

where $N\ge 3$, $1<p<N$. Under some suitable conditions, we prove that the above equation has a nontrivial positive solution by variational methods. To some extent, our results improve and supplement some existing relevant results.