Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity

  • Antonio Ambrosetti

    SISSA, Trieste, Italy
  • Veronica Felli

    Università degli Studi di Milano-Bicocca, Italy
  • Andrea Malchiodi

    Scuola Normale Superiore, Pisa, Italy

Abstract

We deal with a class on nonlinear Schrödinger equations (NLS) with potentials , , and , . Working in weighted Sobolev spaces, the existence of ground states belonging to is proved under the assumption that for some . Furthermore, it is shown that are spikes concentrating at a minimum of , where .

Cite this article

Antonio Ambrosetti, Veronica Felli, Andrea Malchiodi, 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