講座主題：Standing waves with prescribed mass for NLS with competing van der Waals type potentials
專家姓名：孫俊濤
工作單位：山東理工大學
講座時間：2024年12月13日14:30-15:30
講座地點：數學院大會議室341
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
孫俊濤，博士、二級教授、博導，山東理工大學數學與統計學院執行院長，泰山學者青年專家，山東省杰青，山東省優秀研究生指導教師。主要從事偏微分方程、動力系統的理論研究，在SIAM J. Math. Anal.、Stud. Appl. Math.、J. Differential Equations、Nonlinearity、Sci. China Math.等國內外知名數學期刊發表SCI論文50余篇, 主持（完成）國家自然科學基金面上項目、青年基金，山東省杰青等省部級以上項目9項，獲2018年度山東省自然科學二等獎（排名1）。
