TY - JOUR
AU - Aires, Jose
AU - Souto, Marco A. S.
PY - 2015/12/01
Y2 - 2022/01/22
TI - Equation with positive coefficient in the quasilinear term and vanishing potential
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 46
IS - 2
SE -
DO - 10.12775/TMNA.2015.069
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2015.069
SP - 813 - 834
AB - 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 $\kappa > 0$ and the potential can vanish at infinity.<br /><br />
ER -