2022年第5期第43讲：谢华飞博士后学术报告

广州数学大讲坛第五期

第四十三讲——华中师范大学谢华飞博士后学术报告

题目：Qualitative analysis to an eigenvalue problem of the Hénon problem

时间：2022年8月26日（周五）上午9：00-12：00

地点：腾讯会议(会议ID：342 360 785)

报告人：谢华飞博士后

摘要: In this paper, we consider an eigenvalue problem related to Hénon equation. By using various local Pohozaev identities and blow-up analysis, we give some asymptotic behaviour of the first N+2 eigenvalues and corresponding eigenfunctions. As consequences, we obtain the non-degeneracy and local uniqueness of the single peaked solution of the Hénon problem. Moreover, we also have that the Morse index of the single peaked solution is N+1, which gives an affirmative answer to a conjecture raised by Gladiali and Grossi in [J. Differential Equation 253, 2616-2645 (2012)]

报告人简介：

报告人谢华飞博士毕业于北京师范大学数学科学学院，师从唐仲伟教授；目前在华中师范大学数学与统计学学院做博士后，合作导师严树森教授。 谢华飞博士的主要兴趣为非线性偏微分方程解的存在性及其性态的研究。 目前在Calc. Var. Partial Differential Equations,Z. Angew. Math. Phys., NoDEA Nonlinear Differential Equations Appl., Adv. Nonlinear Stud.等杂志上发表论文多篇