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Finite Morse Index Solutions of a Nonlinear Schr?dinger Equation

作     者:Phuong LE Phuong LE

作者机构:Faculty of Economic MathematicsUniversity of Economics and LawHo Chi Minh CityVietnam Vietnam National UniversityHo Chi Minh CityVietnam 

出 版 物:《Acta Mathematica Sinica,English Series》 (数学学报(英文版))

年 卷 期:2023年第39卷第3期

页      面:513-522页

核心收录:

学科分类:07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基  金:Supported by University of Economics and Law VNU-HCM 

主  题:Schrodinger equation Liouville type theorems stable solutions finite Morse index solutions monotonicity formula 

摘      要:We prove Liouville type theorems for stable and finite Morse index H_(loc)^(1)∩L_(loc)^(∞)solutions of the nonlinear Schrodinger equation -Δu+λ|x|^(a)u=|x|b|^(u)|^(p-1)u in R^(N),where N≥2,λ0,a,b-2 and p1,Our analysis reveals that all stable solutions of the equation must be zero for all p1,Furthermore,finite Morse index solutions must be zero if N≥3 an p≥(N+2+2b)/(N-2).The main tools we use are integral estimates,a Pohozaev type identity and a monotonicity formula.

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