@article{Aires_Souto_2015, title={Equation with positive coefficient in the quasilinear term and vanishing potential}, volume={46}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2015.069}, DOI={10.12775/TMNA.2015.069}, abstractNote={In this paper we study the existence of nontrivial classical solution for<br />the quasilinear Schr\"odinger equation: <br />$$ - \Delta u +V(x)u+\frac{\kappa}{2}\Delta<br />(u^{2})u= f(u), <br />$$%<br />in $\mathbb{R}^N$, where $N\geq 3$, $f$ has<br />subcritical growth and $V$ is a nonnegative potential. For this purpose, we use variational methods combined with perturbation arguments, penalization technics of Del Pino and Felmer and Moser iteration. As a main novelty with respect to some previous results, in our work we are able to deal with the case $\kappa &gt; 0$ and the potential can vanish at infinity.<br /><br />}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Aires, Jose and Souto, Marco A. S.}, year={2015}, month={Dec.}, pages={813–834} }