JournalsjemsVol. 8, No. 2pp. 217–228

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
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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].

Cite this article

Jaeyoung Byeon, Zhi-Qiang Wang, Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials. J. Eur. Math. Soc. 8 (2006), no. 2, pp. 217–228

DOI 10.4171/JEMS/48