Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential

Advances in Nonlinear Analysis

article

Jingjing Pan¹  Jian Zhang¹ 

[1] School of Mathematical Sciences, University of Electronic Science and Technology of China;V.C.& V.R. Key Lab of Sichuan Provence, Sichuan Normal University

关键词: variable coefficient nonlinear Schrödinger equation;    minimal mass blow-up solutions;    variational characterization;    ground state;    compactness;   

DOI  :  10.1515/anona-2020-0185

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

This paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem. Then we prove a compactness result by the variational characterization of the ground state solutions. In addition, we construct the blow-up solutions at the minimal mass threshold and further prove the uniqueness result on the minimal mass blow-up solutions which are pseudo-conformal transformation of the ground states.

【 授权许可】

CC BY