Using variational methods combined with perturbation arguments, we study the existence of nontrivial classical solution for the quasilinear Schr\"{ o}dinger equation \begin{ equation*}\label{ 1.1} -\Delta u+ V(x)u+ \frac{ \kappa}{ 2}[\Delta |u|^2]u=l(u),\ x\in\mathbb{ R}^N, \end{ equation*} where $V:\mathbb{ R}^N\rightarrow \mathbb{ R}$ and $l:\mathbb{ R} \to \mathbb{ R}$ are continuous function, $\kappa$ is a parameter and $N\geq 3$. This model has been proposed in plasma physics and nonlinear optics. As a main novelty with respect to some previous results, we are able to deal with the case $\kappa>0$.
Categories: math.AP