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

Jaeyoung Byeon, Zhi-Qiang Wang

• 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-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].