报告人：唐谟勋（Department of Mathematics, Michigan State University）

报告时间：2026年4月29日（周三）下午14:30 - 15:30

报告地点：国交二号楼201会议室

报告摘要：In this talk, I will present a positive resolution of the conjecture of Berestycki and Lions (1983) concerning the uniqueness of bound states to \Delta u +f(u)=0 in R^n, u\in H^1(R^n), u\not\equiv 0, n\ge 3. For the model nonlinearity f(u)=-u+|u|^{p-1}u, 1<p<(n+2)/(n-2), which arises in the study of standing waves for the nonlinear Klein-Gordon equation and the nonlinear Schr\"odinger equation, we show that for each integer k\ge 1, the problem admits a unique solution u=u(|x|), up to translation and reflection, having exactly k zeros for |x|>0. This result appears in Invent. math. 243 245--291 (2026). Further related open problems will also be discussed.

专家简介: 美籍华裔数学家，现任美国密歇根州立大学数学系教授，主要研究领域为非线性椭圆方程与数学生物学，于2025年在数学顶刊《Inventiones Mathematicae》发表独作成果，解决了Berestycki和Lions提出的困扰学界四十年的猜想。