Abstract
In this paper we study the existence of nontrivial classical solution for the quasilinear Schrödinger 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 $\kappa \ge 0$ and the potential can vanish at infinity.
Citation
Jose F.L. Aires. Marco A.S. Souto. "Equation with positive coefficient in the quasilinear term and vanishing potential." Topol. Methods Nonlinear Anal. 46 (2) 813 - 833, 2015. https://doi.org/10.12775/TMNA.2015.069
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