Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity
Antonio Ambrosetti
SISSA, Trieste, ItalyAndrea Malchiodi
Scuola Normale Superiore, Pisa, ItalyVeronica Felli
Università degli Studi di Milano-Bicocca, Italy

Abstract
We deal with a class on nonlinear Schr\"odinger equations \eqref{eq:1} with potentials , , and , . Working in weighted Sobolev spaces, the existence of ground states belonging to is proved under the assumption that satisfies \eqref{eq
}. Furthermore, it is shown that are {\em spikes} concentrating at a minimum of , where .Cite this article
Antonio Ambrosetti, Andrea Malchiodi, Veronica Felli, Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. J. Eur. Math. Soc. 7 (2005), no. 1, pp. 117–144
DOI 10.4171/JEMS/24