Journal of the European Mathematical Society


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Volume 8, Issue 2, 2006, pp. 217–228
DOI: 10.4171/JEMS/48

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

Jaeyoung Byeon[1] and Zhi-Qiang Wang[2]

(1) Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, 305-701, DAEJEON, SOUTH KOREA
(2) Department of Mathematics and Statistics, Utah State University, UT 84322, LOGAN, UNITED STATES

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].

Keywords: Nonlinear Schrödinger Equations, critical frequency, concentrations on spheres

Byeon J, Wang Z. Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials. J. Eur. Math. Soc. 8 (2006), 217-228. doi: 10.4171/JEMS/48