GLOBAL WELL-POSEDNESS BELOW THE GROUND STATE FOR THE NONLINEAR SCHRODINGER EQUATION WITH A LINEAR POTENTIAL

被引：4

作者：

Hamano, Masaru ^{[1
]}

Ikeda, Masahiro ^{[2
,3
]}

机构：

[1] Saitama Univ, Grad Sch Sci & Engn, Dept Math, Sakura Ku, Shimo Okuba 255, Saitama, Saitama 3388570, Japan

[2] Keio Univ, Dept Math, Fac Sci & Technol, Kohoku Ku, 3-14-1 Hiyoshi, Yokohama, Kanagawa 2238522, Japan

[3] RIKEN, Ctr Adv Intelligence Project, Tokyo, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 148卷 / 12期

基金：

日本学术振兴会;

关键词：

Nonlinear Schrodinger equation; standing wave; global well-posedness; BLOW-UP; SCATTERING;

D O I：

10.1090/proc/15161

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study existence of a standing wave solution for the nonlinear Schrodinger equation with a real-valued linear potential in energy-subcritical. Moreover, we also prove global well-posedness to the Cauchy problem with the initial data, whose action is less than that of the ground state with the potential. Hong [Commun. Pure Appl. Anal. 15 (2016), pp. 1571-1601] and the authors showed a scattering result for the problem with the initial data, whose action is less than that of the ground state without the potential. It was noted that the action of the ground state with the potential is greater than that of the ground state without the potential. Our new contribution enables us to treat initial data, which were not treated in those papers.

引用

页码：5193 / 5207

页数：15

共 21 条

[1] Blowup and scattering problems for the nonlinear Schrodinger equations [J].