Equation with positive coefficient in the quasilinear term and vanishing potential - Aires, Jose; Souto, Marco A. S. (Topological Methods in Nonlinear Analysis, 2015)
In this paper we study the existence of nontrivial classical solution for the quasilinear Schr"odinger equation: - Δ u +V(x)u+κ2Δ (u^2)u= f(u), % in R^N, where N≥ 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 κ > 0 and the potential can vanish at infinity.