Standing waves for Schrodinger equation with Kato-Rellich potentials

主讲人：Aleksander Cwiszewski，Professor at Nicolaus Copernicus University

时间：2024年7月13日15:30

地点：三号楼332室

举办单位：数理学院

主讲人介绍：Professor Aleksander Cwiszewski is an excellent young mathematician in nonlinear analysis, PDEs and infinite-dimensional dynamical systems. He has got his doctor degree from Mathematics, Nicolaus Copernicus University (with honors), June 2003, under the supervision by another famous mathematician, Professor Wojciech Kryszewski. Now Aleksander is a full Professor at NCU, Poland. He has published more than 40 papers in SCI journals with high quality, and served as an associated editor of the classical international mathematical journal Topological Methods in Nonlinear Analysis and the Secretary of Scientific Council of Juliusz Schauder Center for Nonlinear Studies.

内容介绍：We shall look for standing waves in the nonlinear Schrodinger equation with a potential belonging to the so-called Kato-Rellich class. The nonlinearity is assumed to satisfy either the Landesman-Lazer conditions or the sign conditions. We prove the existence and bifurcation from infinity results under different types of bounds for the nonlinearity. The results are obtained via the Conley index in the version of Rybakowski and involve tail estimate techniques applied to the parabolic semiflow associated with the problem.