Finite Morse Index Solutions of a Nonlinear Schr?dinger Equation

被引：0

作者：

Phuong LE ^{[1
,2
]}

机构：

[1] Faculty of Economic Mathematics,University of Economics and Law

[2] Vietnam National University

来源：

Acta Mathematica Sinica,English Series | 2023年 / 03期

关键词：

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

We prove Liouville type theorems for stable and finite Morse index Hloc1∩Lloc∞ solutions of the nonlinear Schr?dinger equation-Δu+λ|x|au=|x|b|u|p-1u in RN,where N≥2,λ>0,a,b>-2 and p>1,Our analysis reveals that all stable solutions of the equation must be zero for all p>1,Furthermore,finite Morse index solutions must be zero if N≥3an p≥（N+2+2b）/（N-2）.The main tools we use are integral estimates,a Pohozaev type identity and a monotonicity formula.

引用

页码：513 / 522

页数：10

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