On nonlinear Schrödinger equations with attractive inverse-power potentials

2019/03/11 by Dinh, Van Duong
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.04636

Abstract

We study the Cauchy problem for nonlinear Schrödinger equations with attractive inverse-power potentials. By using variational arguments, we first determine a sharp threshold of global well-posedness and blow-up for the equation in the mass-supercritical case. We next study the existence and non-existence of minimizers for the energy functional with prescribed mass constraint. In the mass-critical case, we also study the blow-up behavior of minimizers when the mass tends to a critical value.

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