双曲空间上非线性薛定谔方程孤子的存在性与稳定性
偏微分方程分析
2015-05-13 v5
摘要
我们研究了双曲空间上非线性驻波方程的基态解或孤子的存在性与稳定性。集中紧性方法适用，并表明结果与欧几里得空间的结果密切相关。
引用
@article{arxiv.0905.1848,
title = {Existence and stability of solitons for the nonlinear Schr\"odinger equation on hyperbolic space},
author = {Hans Christianson and Jeremy Marzuola},
journal= {arXiv preprint arXiv:0905.1848},
year = {2015}
}
备注
New: As noted in Banica-Duyckaerts (arXiv:1411.0846), Section 5 should read that for sufficiently large mass, sub-critical problems can be solved via energy minimization for all d \geq 2 and as a result Cazenave-Lions results can be applied in Section 6 with the same restriction. These requirements were addressed by the subsequent work with Metcalfe and Taylor in arXiv:1203.3612