JournalsjemsVol. 8 , No. 2DOI 10.4171/jems/48

Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials

  • Jaeyoung Byeon

    KAIST, Daejeon, South Korea
  • Zhi-Qiang Wang

    Utah State University, Logan, United States
Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials cover

Abstract

For singularly perturbed Schr\"odinger equations with decaying potentials at infinity we construct semiclassical states of a critical frequency concentrating on spheres near zeroes of the potentials. The results generalize some recent work of Ambrosetti-Malchiodi-Ni[3] which gives solutions concentrating on spheres where the potential is positive. The solutions we obtain exhibit different behaviors from the ones given in [3].