Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential

被引：4

作者：

Mukherjee, Debangana ^{[1
]}

Phan Thanh Nam ^{[2
,3
]}

Phuoc-Tai Nguyen ^{[1
]}

机构：

[1] Masaryk Univ, Dept Math & Stat, Brno, Czech Republic

[2] Ludwig Maximilians Univ Munchen, Dept Math, Theresienstr 39, D-80333 Munich, Germany

[3] Munich Ctr Quantum Sci & Technol MCQST, Schellingstr 4, D-80799 Munich, Germany

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2021年 / 281卷 / 05期

关键词：

Nonlinear Schrodinger equation; Inverse square potential; Hardy-Gagliardo-Nirenberg inequality; Ground state solutions; NONLINEAR SCHRODINGER-EQUATIONS; POSITIVE RADIAL SOLUTIONS; SCATTERING; EXISTENCE; WAVE;

D O I：

10.1016/j.jfa.2021.109092

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the focusing nonlinear Schrodinger equation with the critical inverse square potential. We give the first proof of the uniqueness of the ground state solution. Consequently, we obtain a sharp Hardy-Gagliardo-Nirenberg interpolation inequality. Moreover, we provide a complete characterization for the minimal mass blow-up solutions to the time dependent problem. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：45

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