Standing waves for Schrodinger equation with Kato-Rellich potentials

报告摘要：

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.

报告人简介：ProfessorAleksander Cwiszewskiis 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, ProfessorWojciech 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 journalTopological Methods in Nonlinear Analysisand the Secretary of Scientific Council of Juliusz Schauder Center for Nonlinear Studies.