Finite Morse Index Solutions of a Nonlinear Schr?dinger Equation
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.