Positive solution to quasilinear Schrodinger equations via Orlicz space framework

This article concerns the existence of solutions for the generalized quasilinear Schrodinger equation$$ -\hbox{div}(g^2(u)\nabla u)+g(u)g'(u){|\nabla u|}^2+V(x)u=f(x,u),\quad x\in\mathbb{R}^N\,. $$ We obtain a positive solution by using a change of variables and a minimax theorem in an Orlicz space framework.