Lecture: WOJCIECH KRYSZEWSKI, 15:00-16:00, 30, August, Nicolaus Copernicus University

Date：2018-08-22Views：273

Title：GENERALIZED NEHARI MANIFOLD AND SEMILINEAR SCHRÖDINGER EQUATION

Abstract We study the Schrödinger equations u+ V (x)u = f(x; u) in and

u-λu = f(x; u)in a bounded domain. We assume that f is superlinear but

of subcritical growth and

is nondecreasing. In

we also assume that V and f are periodic in

. We show that these equations have a ground state and that there exist infinitely many solutions if f is odd in u. The results generalize those od Szulkin and Weth, where

was assumed to be strictly increasing. This seemingly small change forces us to go beyond methods of smooth analysis. The work is joint with F. de Paiva and A. Szulkin.

Introduction: Prof. Wojciech Kryszewski is a professor of Nicolaus Copernicus University, Poland, and a managing editor of the journal: Topological Methods in Nonlinear Analysis published by the Schauder Center for Nonlinear Studies. He is also a director of the Schauder Center for Nonlinear Studies. His main research interests are functional analysis, nonlinear analysis, semigroup theory, nonlinear partial differential equations, and so on. He has published about 60 papers in the journals such as: Trans. Amer. Math. Soc.、Topol. Methods Nonlinear Anal.、SIAM J. Control Optim.、Proc. Amer.Math. Soc..