Uniqueness of bound states to Δu - u+|u|p-1 u=0 in Rn, n ≥ 3

• 成果类型: Article; Early Access
• 署名作者: Tang, Moxun
• 署名单位: Michigan State University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01379-0
• 发表日期: 2025
• 关键词: positive radial solutions; scalar field-equations; ground-states; EXISTENCE; delta-u+f(u)=0; diffusion; nonuniqueness; multiplicity

摘要

We give a positive answer to a conjecture of Berestycki and Lions in 1983 on the uniqueness of bound states to Delta u+f(u)=0 in R-n, u is an element of H1(R-n), u not equivalent to 0, n >= 3 . For the model nonlinearity f(u)=-u+|u|(p-1)u1 <(n+2)/(n-2), arising from finding standing waves of Klein-Gordon equation or nonlinear Schrodinger equation, we show that, for each integer k >= 1, the problem has a unique solution u=u(|x|),x is an element of & Ropf;(n), up to translation and reflection, that has precisely k zeros for |x|>0