Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials
Jaeyoung Byeon
KAIST, Daejeon, South KoreaZhi-Qiang Wang
Utah State University, Logan, United States
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Abstract
For singularly perturbed Schrödinger 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–Malchiod–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