报告题目：Variational problem with repulsive-attractive kernels and its application

报告时间：2026年3月24日下午2点30分

报告地点：腾讯会议776 901 572

报告摘要：We focus on standing waves with prescribed mass for the Hartree equation with repulsive-attractive kernels, which are used in particle physics to describe the nonlocal interaction among particles. First, we consider a family of interaction functionals consisting of power-law potentials with attractive and repulsive parts and establish the existence of global minimizers. By relaxing the uniform boundedness and radial symmetry conditions, we prove a conjecture raised by Choksi-Fetecau-Topaloglu. Then as an application, based on classification of attractive part in the kernel, a complete study on existence and qualitative analysis of standing waves for the Hartree equation with repulsive-attractive kernels are given.

报告人简介：罗肖，合肥工业大学数学学院副教授，博士生导师。主要研究领域为非线性泛函分析及其在偏微分方程、数学物理等方面的应用。先后在质量约束变分理论及泛函结构不定问题的新理论性框架和工具的建立方面取得系统性研究成果，在Math. Ann.、J. Funct. Anal.、SIAM J. Math. Anal.、Israel J. Math.、Math. Z.、 Calc. Var. Partial Differential Equations、J. Differential Equations、中国科学英文版等国内外期刊发表学术论文三十余篇。正在主持国家自然科学基金面上项目和安徽省自然科学基金面上项目，曾主持完成国家自然科学基金青年科学基金项目。2023年荣获安徽省青年数学奖。

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