On nonlinear Schr\"odinger equations with attractive inverse-power potentials
Analysis of PDEs
2020-01-06 v3
Abstract
We study the Cauchy problem for nonlinear Schr\"odinger 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.
Keywords
Cite
@article{arxiv.1903.04636,
title = {On nonlinear Schr\"odinger equations with attractive inverse-power potentials},
author = {Van Duong Dinh},
journal= {arXiv preprint arXiv:1903.04636},
year = {2020}
}
Comments
25 pages