### Equation with positive coefficient in the quasilinear term and vanishing potential

DOI: http://dx.doi.org/10.12775/TMNA.2015.069

#### Abstract

the quasilinear Schr\"odinger equation:

$$ - \Delta u +V(x)u+\frac{\kappa}{2}\Delta

(u^{2})u= f(u),

$$%

in $\mathbb{R}^N$, where $N\geq 3$, $f$ has

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 $\kappa > 0$ and the potential can vanish at infinity.

#### Keywords

#### References

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