讲座主题：Standing waves with prescribed mass for NLS with competing van der Waals type potentials

专家姓名：孙俊涛

工作单位：山东理工大学

讲座时间：2024年12月13日14:30-15:30

讲座地点：数学院大会议室341

主办单位：烟台大学数学与信息科学学院

内容摘要：

In this talk, we investigate standing waves with prescribed mass for a class of Schrodinger equations with competing Van Der Waals type potentials, arising in a model of non-relativistic bosonic atoms and molecules. By developing an approach based on a direct minimization of the energy functional on a new constrained manifold, we establish the existence of two normalized solutions for the corresponding stationary problem. One is a local minimizer with positive level and the other one is a global minimizer with negative level. Moreover, we find that the global minimizer is farther away from the origin than the local minimizer. Finally, we explore the relations between the ground state solution and the least action solution, and some dynamical behavior and scattering results are presented as well.

主讲人介绍：

孙俊涛，博士、二级教授、博导，山东理工大学数学与统计学院执行院长，泰山学者青年专家，山东省杰青，山东省优秀研究生指导教师。主要从事偏微分方程、动力系统的理论研究，在SIAM J. Math. Anal.、Stud. Appl. Math.、J. Differential Equations、Nonlinearity、Sci. China Math.等国内外知名数学期刊发表SCI论文50余篇, 主持（完成）国家自然科学基金面上项目、青年基金，山东省杰青等省部级以上项目9项，获2018年度山东省自然科学二等奖（排名1）。