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(xué)
講座時(shí)間：2024年12月13日14:30-15:30
講座地點(diǎn)：數(shù)學(xué)院大會(huì)議室341
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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(jí)教授、博導(dǎo)，山東理工大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院執(zhí)行院長(zhǎng)，泰山學(xué)者青年專家，山東省杰青，山東省優(yōu)秀研究生指導(dǎo)教師。主要從事偏微分方程、動(dòng)力系統(tǒng)的理論研究，在SIAM J. Math. Anal.、Stud. Appl. Math.、J. Differential Equations、Nonlinearity、Sci. China Math.等國(guó)內(nèi)外知名數(shù)學(xué)期刊發(fā)表SCI論文50余篇, 主持（完成）國(guó)家自然科學(xué)基金面上項(xiàng)目、青年基金，山東省杰青等省部級(jí)以上項(xiàng)目9項(xiàng)，獲2018年度山東省自然科學(xué)二等獎(jiǎng)（排名1）。
