EQUATION WITH POSITIVE COEFFICIENT IN THE QUASILINEAR TERM AND VANISHING POTENTIAL

作者：Aires Jose F L^*; Souto Marco A S

来源：Topological Methods in Nonlinear Analysis, 2015, 46(2): 813-833.

DOI：10.12775/tmna.2015.069

• Quasilinear Schrodinger equation
• subcritical growth
• vanishing potentials

In this paper we study the existence of nontrivial classical solution for the quasilinear Schrodinger equation:
-Delta u + V(x)u + k/2 Delta(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 k > 0 and the potential can vanish at infinity.

• 出版日期2015-12