讲座题目：Nondegeneracy of positive solutions for a biharmonic hartree equation and its applications

主办单位：三峡数学研究中心/理学院

报告专家：杨敏波教授

报告时间：2023.11.9（星期四） 上午 9:00

报告地点：腾讯会议 （ID: 756-430-697）

专家简介：杨敏波，浙江师范大学数学系教授，博士生导师，主要研究非线性分析与偏微分方程，近年来在Calc. Var. Partial Differential Equations、Mathematische Zeitschrift、Commun. Anal. Geom.、J. Differential Equations、Nonlinearity、中国科学（中、英）等国内外高水平学术期刊上录用发表论文80余篇。

报告摘要：In this talk, we introduced some prolbems related to the biharmonic hartree equation. First, by using the spherical harmonic decomposition and the Funk-Heck formula of the spherical harmonic function, we prove the nondegeneracy of the positive solutions for the above equation. Then as applications, we investigate the stability of a type of nonlocal Sobolev inequality and give the gradient form remainder. Moreover, by applying a finite dimension reduction and local Pohoaev identity, we can also construct multi-bubble solutions for the equation with potential. We will show what is the role fo the dimension and the order of the Riesz potential in proving the existence result. In fact, the existence result is restricted to the range , .